3-1 Numeration Systems - Dr. Travers Page of...
Transcript of 3-1 Numeration Systems - Dr. Travers Page of...
![Page 1: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/1.jpg)
§ 3-1 Numeration Systems
![Page 2: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/2.jpg)
How We Use Numbers
cardinal numbers
how many numbers are in a setordinal numbers
positionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 3: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/3.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numberspositionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 4: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/4.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numbers
positionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 5: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/5.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numberspositionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 6: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/6.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numberspositionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 7: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/7.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numberspositionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 8: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/8.jpg)
How We Use Numbers
cardinal numbershow many numbers are in a set
ordinal numberspositionwhich comes first
identification numbers
Numbers are abstract ideas for children to understand, so it isimportant to find symbolic ways to represent them to help them graspthe concept.
![Page 9: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/9.jpg)
Our Number System
What is the base of our number system?
Why do we have a base 10 number system?
It is useful to talk of other civilizations’ systems when dealing withchildren to help them understand the ideas that lead to thedevelopment of these systems.
![Page 10: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/10.jpg)
Our Number System
What is the base of our number system?
Why do we have a base 10 number system?
It is useful to talk of other civilizations’ systems when dealing withchildren to help them understand the ideas that lead to thedevelopment of these systems.
![Page 11: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/11.jpg)
Our Number System
What is the base of our number system?
Why do we have a base 10 number system?
It is useful to talk of other civilizations’ systems when dealing withchildren to help them understand the ideas that lead to thedevelopment of these systems.
![Page 12: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/12.jpg)
The Tally System
![Page 13: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/13.jpg)
The Tally System
Propertiesmost simplistic
a line represents 1, crossing represents 5
grouping is to make counting easier
very tedious
additive system
![Page 14: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/14.jpg)
The Tally System
Propertiesmost simplistic
a line represents 1, crossing represents 5
grouping is to make counting easier
very tedious
additive system
![Page 15: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/15.jpg)
The Tally System
Propertiesmost simplistic
a line represents 1, crossing represents 5
grouping is to make counting easier
very tedious
additive system
![Page 16: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/16.jpg)
The Tally System
Propertiesmost simplistic
a line represents 1, crossing represents 5
grouping is to make counting easier
very tedious
additive system
![Page 17: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/17.jpg)
The Tally System
Propertiesmost simplistic
a line represents 1, crossing represents 5
grouping is to make counting easier
very tedious
additive system
![Page 18: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/18.jpg)
The Egyptian Numeration System
![Page 19: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/19.jpg)
The Egyptian Numeration System
![Page 20: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/20.jpg)
The Egyptian Numeration System
Propertiesbase 10 system
additive system
multiple symbols is an improvement
order does not matter
![Page 21: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/21.jpg)
The Egyptian Numeration System
Propertiesbase 10 system
additive system
multiple symbols is an improvement
order does not matter
![Page 22: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/22.jpg)
The Egyptian Numeration System
Propertiesbase 10 system
additive system
multiple symbols is an improvement
order does not matter
![Page 23: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/23.jpg)
The Egyptian Numeration System
Propertiesbase 10 system
additive system
multiple symbols is an improvement
order does not matter
![Page 24: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/24.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWhat decimal number is represented here?
2008
![Page 25: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/25.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWhat decimal number is represented here?
2008
![Page 26: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/26.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWhat decimal number is represented here?
2,320,111
![Page 27: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/27.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWhat decimal number is represented here?
2,320,111
![Page 28: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/28.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWrite the number 245 using Egyptian hieroglyphics.
![Page 29: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/29.jpg)
Examples Using Egyptian Hieroglyphics
ExampleWrite the number 245 using Egyptian hieroglyphics.
![Page 30: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/30.jpg)
The Roman Numeration System
Decimal Roman1
I5 V10 X50 L100 C500 D
1000 M
Where do we see Roman numerals in modern day?
![Page 31: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/31.jpg)
The Roman Numeration System
Decimal Roman1 I5
V10 X50 L100 C500 D
1000 M
Where do we see Roman numerals in modern day?
![Page 32: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/32.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10
X50 L100 C500 D
1000 M
Where do we see Roman numerals in modern day?
![Page 33: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/33.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50
L100 C500 D
1000 M
Where do we see Roman numerals in modern day?
![Page 34: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/34.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50 L100
C500 D
1000 M
Where do we see Roman numerals in modern day?
![Page 35: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/35.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50 L100 C500
D1000 M
Where do we see Roman numerals in modern day?
![Page 36: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/36.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50 L100 C500 D1000
M
Where do we see Roman numerals in modern day?
![Page 37: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/37.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50 L100 C500 D1000 M
Where do we see Roman numerals in modern day?
![Page 38: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/38.jpg)
The Roman Numeration System
Decimal Roman1 I5 V10 X50 L100 C500 D1000 M
Where do we see Roman numerals in modern day?
![Page 39: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/39.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 40: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/40.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 41: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/41.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 42: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/42.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that number
M = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 43: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/43.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 44: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/44.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 45: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/45.jpg)
The Roman Numeration System
Propertiesnot a base 10 system
additive system
subtractive system
multiplicative - we place a bar over a number to represent 1000times that numberM = 1, 000, 000
positional system - where we place the symbols changes thevalue
VI=6 IV=4
![Page 46: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/46.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2
II2 4 IV3 9 IX4 40 XL5 49 XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 47: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/47.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4
IV3 9 IX4 40 XL5 49 XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 48: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/48.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9
IX4 40 XL5 49 XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 49: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/49.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9 IX4 40
XL5 49 XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 50: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/50.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9 IX4 40 XL5 49
XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 51: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/51.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9 IX4 40 XL5 49 XLIX6 99
XCIX7 1489 MCDLXXXIX
![Page 52: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/52.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9 IX4 40 XL5 49 XLIX6 99 XCIX7 1489
MCDLXXXIX
![Page 53: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/53.jpg)
More Roman Numerals
ExampleWrite the following using Roman numerals.
1 2 II2 4 IV3 9 IX4 40 XL5 49 XLIX6 99 XCIX7 1489 MCDLXXXIX
![Page 54: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/54.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII
4232 DCXIV 6143 CCII 200,002
![Page 55: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/55.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII 423
2 DCXIV 6143 CCII 200,002
![Page 56: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/56.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII 4232 DCXIV
6143 CCII 200,002
![Page 57: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/57.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII 4232 DCXIV 614
3 CCII 200,002
![Page 58: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/58.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII 4232 DCXIV 6143 CCII
200,002
![Page 59: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/59.jpg)
More Roman Numerals
ExampleWrite the following as decimal numbers.
1 CDXXIII 4232 DCXIV 6143 CCII 200,002
![Page 60: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/60.jpg)
The Babylonian Numeration System
![Page 61: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/61.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 62: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/62.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 63: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/63.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 64: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/64.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 65: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/65.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 66: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/66.jpg)
The Babylonian Numeration System
For the sake of simplicity, we will use symbols that look like thefollowing:
Propertiesbase 60 system
additive system
multiplicative
place valued system
positional
![Page 67: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/67.jpg)
The Babylonian Numeration System
Base 60
603 602 601 600
ExampleWrite 53 using Babylonian cuneiform.
![Page 68: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/68.jpg)
The Babylonian Numeration System
Base 60
603 602 601 600
ExampleWrite 53 using Babylonian cuneiform.
![Page 69: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/69.jpg)
The Babylonian Numeration System
Base 60
603 602 601 600
ExampleWrite 53 using Babylonian cuneiform.
![Page 70: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/70.jpg)
The Babylonian Numeration System
ExampleWhat decimal number is represented here?
ExampleWhat decimal number is represented here?
![Page 71: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/71.jpg)
The Babylonian Numeration System
ExampleWhat decimal number is represented here?
ExampleWhat decimal number is represented here?
![Page 72: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/72.jpg)
The Babylonian Numeration System
ExampleWhat decimal number is represented here?
The Babylonians realized they needed a place holder to represent thatthey had a place with nothing in it when writing their numbers.
![Page 73: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/73.jpg)
The Babylonian Numeration System
ExampleWhat decimal number is represented here?
The Babylonians realized they needed a place holder to represent thatthey had a place with nothing in it when writing their numbers.
![Page 74: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/74.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 75: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/75.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 76: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/76.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 77: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/77.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 78: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/78.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 79: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/79.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 80: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/80.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 81: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/81.jpg)
The Babylonian Numeration System
ExampleWrite 3821 using Babylonian cuneiform.
To figure this out, we want to write this in expanded form. What is thelargest power of 60 that goes into 3821?
602( ) + 601( ) + 600( )
602(1) + 601( ) + 600( )
602(1) + 601(3) + 600( )
602(1) + 601(3) + 600(41)
![Page 82: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/82.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 83: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/83.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 84: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/84.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 85: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/85.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 86: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/86.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 87: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/87.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 88: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/88.jpg)
The Babylonian Numeration System
ExampleWrite 7205 using Babylonian cuneiform.
What is the largest power of 60 that goes into 7205?
7205 = 602( ) + 601( ) + 600( )
= 602(2) + 601( ) + 600( )
= 602(2) + 601(0) + 600( )
= 602(2) + 601(0) + 600(5)
![Page 89: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/89.jpg)
The Mayan Numeration System
Properties1 additive system2 multiplicative system3 positional system4 place valued system5 symbol for 0
![Page 90: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/90.jpg)
The Mayan Numeration System
Properties1 additive system
2 multiplicative system3 positional system4 place valued system5 symbol for 0
![Page 91: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/91.jpg)
The Mayan Numeration System
Properties1 additive system2 multiplicative system
3 positional system4 place valued system5 symbol for 0
![Page 92: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/92.jpg)
The Mayan Numeration System
Properties1 additive system2 multiplicative system3 positional system
4 place valued system5 symbol for 0
![Page 93: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/93.jpg)
The Mayan Numeration System
Properties1 additive system2 multiplicative system3 positional system4 place valued system
5 symbol for 0
![Page 94: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/94.jpg)
The Mayan Numeration System
Properties1 additive system2 multiplicative system3 positional system4 place valued system5 symbol for 0
![Page 95: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/95.jpg)
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
![Page 96: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/96.jpg)
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
![Page 97: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/97.jpg)
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
![Page 98: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/98.jpg)
The Mayan Numeration System
1’s
20’s
18 · 20’s
18 · 202’s
![Page 99: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/99.jpg)
The Mayan Numeration System
ExampleWrite 7 in Mayan.
• •
ExampleWrite 45 in Mayan.
• •
Spacing is very important ...
![Page 100: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/100.jpg)
The Mayan Numeration System
ExampleWrite 7 in Mayan.
• •
ExampleWrite 45 in Mayan.
• •
Spacing is very important ...
![Page 101: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/101.jpg)
The Mayan Numeration System
ExampleWrite 7 in Mayan.
• •
ExampleWrite 45 in Mayan.
• •
Spacing is very important ...
![Page 102: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/102.jpg)
The Mayan Numeration System
ExampleWrite 7 in Mayan.
• •
ExampleWrite 45 in Mayan.
• •
Spacing is very important ...
![Page 103: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/103.jpg)
The Mayan Numeration System
ExampleWrite 7 in Mayan.
• •
ExampleWrite 45 in Mayan.
• •
Spacing is very important ...
![Page 104: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/104.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 105: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/105.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 106: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/106.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 =
360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 107: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/107.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 108: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/108.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 109: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/109.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 110: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/110.jpg)
The Mayan Numeration System
ExampleWrite 611 in Mayan
First, we need to write 611 in expanded form.
611 = 360 + 251
= 360 + 240 + 11
= 18 · 20 + 12 · 20 + 11
•
• •
•
![Page 111: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/111.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system
2 positional system3 additive system (values for various numerals added)4 multiplicative5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 112: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/112.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system2 positional system
3 additive system (values for various numerals added)4 multiplicative5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 113: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/113.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system2 positional system3 additive system (values for various numerals added)
4 multiplicative5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 114: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/114.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system2 positional system3 additive system (values for various numerals added)4 multiplicative
5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 115: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/115.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system2 positional system3 additive system (values for various numerals added)4 multiplicative5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 116: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/116.jpg)
The Hindu-Arabic Numeration System
Properties1 base 10 system2 positional system3 additive system (values for various numerals added)4 multiplicative5 10 symbols called digits
We can use manipulatives to help children understand how our systemworks. A common manipulative is base 10 blocks.
![Page 117: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/117.jpg)
Other Bases
To see the types of troubles children have with the base 10 system, wewill use numeration systems with different bases.
To do this, we first have to understand what the place values in base10 really mean.We can see this using expanded form.
ExampleWrite 4321 in expanded form.
4321 = 4(1000) + 3(100) + 2(10) + 1(1)
= 4 · 103 + 3 · 102 + 2 · 101 + 1 · 100
![Page 118: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/118.jpg)
Other Bases
To see the types of troubles children have with the base 10 system, wewill use numeration systems with different bases.
To do this, we first have to understand what the place values in base10 really mean.We can see this using expanded form.
ExampleWrite 4321 in expanded form.
4321 = 4(1000) + 3(100) + 2(10) + 1(1)
= 4 · 103 + 3 · 102 + 2 · 101 + 1 · 100
![Page 119: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/119.jpg)
Other Bases
To see the types of troubles children have with the base 10 system, wewill use numeration systems with different bases.
To do this, we first have to understand what the place values in base10 really mean.We can see this using expanded form.
ExampleWrite 4321 in expanded form.
4321 = 4(1000) + 3(100) + 2(10) + 1(1)
= 4 · 103 + 3 · 102 + 2 · 101 + 1 · 100
![Page 120: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/120.jpg)
Other Bases
To see the types of troubles children have with the base 10 system, wewill use numeration systems with different bases.
To do this, we first have to understand what the place values in base10 really mean.We can see this using expanded form.
ExampleWrite 4321 in expanded form.
4321 = 4(1000) + 3(100) + 2(10) + 1(1)
= 4 · 103 + 3 · 102 + 2 · 101 + 1 · 100
![Page 121: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/121.jpg)
Other Bases
To see the types of troubles children have with the base 10 system, wewill use numeration systems with different bases.
To do this, we first have to understand what the place values in base10 really mean.We can see this using expanded form.
ExampleWrite 4321 in expanded form.
4321 = 4(1000) + 3(100) + 2(10) + 1(1)
= 4 · 103 + 3 · 102 + 2 · 101 + 1 · 100
![Page 122: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/122.jpg)
Base 2
Binary is the language of computers and also helps children see placevalue quickly.
ExampleConvert 73 to base 2
The place values for binary are
. . . 27 26 25 24 23 22 21 20
We need to determine what is the highest power of 2 that goes into 73.
![Page 123: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/123.jpg)
Base 2
Binary is the language of computers and also helps children see placevalue quickly.
ExampleConvert 73 to base 2
The place values for binary are
. . . 27 26 25 24 23 22 21 20
We need to determine what is the highest power of 2 that goes into 73.
![Page 124: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/124.jpg)
Base 2
Binary is the language of computers and also helps children see placevalue quickly.
ExampleConvert 73 to base 2
The place values for binary are
. . . 27 26 25 24 23 22 21 20
We need to determine what is the highest power of 2 that goes into 73.
![Page 125: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/125.jpg)
Base 2
Binary is the language of computers and also helps children see placevalue quickly.
ExampleConvert 73 to base 2
The place values for binary are
. . . 27 26 25 24 23 22 21 20
We need to determine what is the highest power of 2 that goes into 73.
![Page 126: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/126.jpg)
Base 2
73 =
1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 127: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/127.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 128: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/128.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 129: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/129.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 130: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/130.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 131: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/131.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 132: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/132.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 133: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/133.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 134: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/134.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 135: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/135.jpg)
Base 2
73 = 1(64) + 9
= 1(64) + 0(32) + 9
= 1(64) + 0(32) + 0(16) + 9
= 1(64) + 0(32) + 0(16) + 1(8) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1
= 1(64) + 0(32) + 0(16) + 1(8) + 0(4) + 0(2) + 1(1)
So, we have 73 = 1001001TWO.
Why do we need to put the subscript ‘TWO’ but not ‘TEN’?
![Page 136: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/136.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 137: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/137.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 138: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/138.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 139: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/139.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 140: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/140.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 =
49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 141: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/141.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 142: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/142.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 143: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/143.jpg)
Base 7
If we are in base 7, what are the first 4 place values?
. . . 73 72 71 70
343 49 7 1
ExampleConvert 321 to base 7.
321 = 49( ) + 7( ) + 1( )
= 49(6) + 7( ) + 1( )
= 49(6) + 7(3) + 6
So, 321 = 636SEVEN .
![Page 144: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/144.jpg)
Base 7
ExampleConvert 219 to base 7.
219 = 432SEVEN
ExampleConvert 693SEVEN to base 10.
DNE ... why?
![Page 145: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/145.jpg)
Base 7
ExampleConvert 219 to base 7.
219 = 432SEVEN
ExampleConvert 693SEVEN to base 10.
DNE ... why?
![Page 146: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/146.jpg)
Base 7
ExampleConvert 219 to base 7.
219 = 432SEVEN
ExampleConvert 693SEVEN to base 10.
DNE ... why?
![Page 147: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/147.jpg)
Base 7
ExampleConvert 219 to base 7.
219 = 432SEVEN
ExampleConvert 693SEVEN to base 10.
DNE ... why?
![Page 148: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/148.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN = 6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 149: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/149.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN = 6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 150: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/150.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN =
6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 151: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/151.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN = 6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 152: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/152.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN = 6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 153: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/153.jpg)
Base 7
ExampleConvert 623SEVEN to base 10.
We again have to think about what the place values represent.
623SEVEN = 6(72) + 2(7) + 3(1)
= 294 + 14 + 3
= 311
![Page 154: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/154.jpg)
Hexadecimal (Base 16)
How can we deal with number systems where we may need to exceed9 in any one position?
10 11 12 13 14 15A B C D E F
![Page 155: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/155.jpg)
Hexadecimal (Base 16)
How can we deal with number systems where we may need to exceed9 in any one position?
10 11 12 13 14 15A B C D E F
![Page 156: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/156.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 157: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/157.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 158: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/158.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 159: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/159.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 160: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/160.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 161: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/161.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 162: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/162.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 163: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/163.jpg)
Hexadecimal
ExampleConvert 352 to hexadecimal.
How do we begin?
. . . 162 161 160
256 16 1
352 = 256( ) + 16( ) + 1( )
= 256(1) + 16( ) + 1( )
= 256(1) + 16(6) + 0
So, 352 = 160HEX .
![Page 164: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/164.jpg)
Hexadecimal
ExampleConvert 792 to hexadecimal.
792 = 318HEX
![Page 165: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/165.jpg)
Hexadecimal
ExampleConvert 792 to hexadecimal.
792 = 318HEX
![Page 166: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/166.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 167: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/167.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 168: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/168.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX =
A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 169: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/169.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 170: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/170.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 171: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/171.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 172: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/172.jpg)
Hexadecimal
ExampleConvert ABCHEX to a decimal number.
Now we are going the other way ...
ABCHEX = A(162) + B(16) + C
= 10(162) + 11(16) + 12
= 2560 + 176 + 12
= 2748
![Page 173: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/173.jpg)
Hexadecimal
ExampleConvert 3EF1HEX to a decimal number.
3EF1HEX = 3(163) + E(162) + F(16) + 1(1)
= 3(4096) + 14(256) + 15(16) + 1
= 16113
![Page 174: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/174.jpg)
Hexadecimal
ExampleConvert 3EF1HEX to a decimal number.
3EF1HEX = 3(163) + E(162) + F(16) + 1(1)
= 3(4096) + 14(256) + 15(16) + 1
= 16113
![Page 175: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/175.jpg)
Hexadecimal
ExampleConvert 3EF1HEX to a decimal number.
3EF1HEX = 3(163) + E(162) + F(16) + 1(1)
= 3(4096) + 14(256) + 15(16) + 1
= 16113
![Page 176: 3-1 Numeration Systems - Dr. Travers Page of Mathbtravers.weebly.com/uploads/6/7/2/9/6729909/3-1_numeration_syste… · Our Number System What is the base of our number system? Why](https://reader033.fdocuments.in/reader033/viewer/2022060609/60601670a7e9f85da32039a7/html5/thumbnails/176.jpg)
Hexadecimal
ExampleConvert 3EF1HEX to a decimal number.
3EF1HEX = 3(163) + E(162) + F(16) + 1(1)
= 3(4096) + 14(256) + 15(16) + 1
= 16113