To show how very large or very small numbers can be expressed in scientific notation
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Transcript of To show how very large or very small numbers can be expressed in scientific notation
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Section 5.1
Scientific Notation and Units
1. To show how very large or very small numbers can be expressed in scientific notation
2. To learn the English, metric, and SI systems of measurement
3. To use the metric system to measure length, volume and mass
Objectives
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Section 5.1
Scientific Notation and Units
“Arithmetic is being able to count up to twenty without taking your shoes off”
Mickey Mouse
Mickey also says “Do you remember what an exponent is?”
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Section 5.1
Scientific Notation and Units
A. Scientific Notation
• Very large or very small numbers can be expressed using scientific notation – The number is written as a number between 1 and 10
multiplied by 10 raised to a power.
e.g. 7200 is 7.2 x 103
– The power of 10 depends on:• The number of places the decimal point is moved.
• The direction the decimal point is moved.
Left Positive exponentRight Negative exponent
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Section 5.1
Scientific Notation and Units
A. Scientific Notation
• Representing Large Numbers
93,000,000 miles from the Earth to the Sun (sunlight takes 8 minutes to reach us)
93,000,000 = 9.3 x 10,000,000= 9.3 x 10 x 10 x 10 x 10 x 10 x 10 x 10= 9.3 x 107 (Decimal point moved 7 digits to the left)
Number between 1 and 10
Appropriate power of ten
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Section 5.1
Scientific Notation and Units
A. Scientific Notation
• Representing Small Numbers
0.000167
To obtain a number between 1 and 10 we must move the decimal point to the right.
0.000167 = 1.67 10-4
10-4 = 1/10000 (one ten-thousandth)
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Section 5.1
Scientific Notation and Units
Convert the following numbers between normal and scientific notation:
329
700,000
20090
0.000034
0.01023
123.4
45.607
1.7 x 103
2.4503 x 105
7.9 x 1011
2.8 x 10-3
7.45 x 10-1
2.3 x 10-7
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Section 5.1
Scientific Notation and Units
Convert the following numbers/sums into correct scientific notation:
35.9 x 103
556.67 x 104
22.7 x 10-3
0.0348 x 10-1
1845 x 105
123.4 x 1023
0.00345 x 107
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Section 5.1
Scientific Notation and Units
Scientific Notation Math - Exponents
103
10-5
100
1/103
1/105
1/10-2
1/10-7
103 x 108
10-3 x 107
10-5 x 10-3
105 / 102
10-7 / 105
10-2 / 10-4
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Section 5.1
Scientific Notation and Units
Scientific Notation Math
Multiplication
- multiply the numbers, add the indices
1.2 x 104 multiplied by 5 x 106 =
Division
- divide the numbers, subtract the indices
5.5 x 108 divided by 1.1 x 102 =
(For all operations reconvert answers to full scientific notation)
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Section 5.1
Scientific Notation and Units
Scientific Notation Math
• Addition or subtraction:
Convert to the same base and perform the operation
Then reconvert to scientific notation
1.04 x 103 plus 6.8 x 102 =
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Section 5.1
Scientific Notation and Units
Combined Operations – Give the answer in scientific notation
7.5 x 105
__________
3 x 103
2 x 106 x 1.5 x 102
________________________
5 x 103
6.5 x 105 x 4 x 104
________________________
2 x 10-3
7.5 x 10-5
______________________
3 x 103 x 5 x 10-6
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Section 5.1
Scientific Notation and Units
B. Units
• Units provide a scale on which to represent the results of a measurement. What units can you think of?
“Time is God’s way of making sure everything doesn’t happen at once” (Unknown)
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Section 5.1
Scientific Notation and Units
B. Units • There are 3 commonly used unit systems.
– English (used in the United States)– Metric (broadly used across the World) – SI (most formal version of Metric used in science)
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Section 5.1
Scientific Notation and Units
Countries not yet officially metric: USA, Liberia, Myanmar
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Section 5.1
Scientific Notation and Units
Metric/SI Prefixes
Prefixes are used to denote different sizes of each unit:
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Section 5.1
Scientific Notation and Units
Full List of Metric Prefixes
Multiplication factor (scientific notation)
Prefix Symbol
(1024) yotta Y
(1021) zetta Z
(1018) exa E
(1015) peta P
(1012) tera T
1 000 000 000 (109) giga G
1 000 000 (106) mega M
1000 (103) kilo k
100 (102) hecto h
10 (101) deka da
0.1 (10-1) deci d
0.01 (10-2) centi c
0.001 (10-3) milli m
0.000 001 (10-6) micro µ
0.000 000 001 (10-9) nano n
(10-12) pico p
(10-15) femto f
(10-18) atto a
(10-21) zepto z
(10-24) yocto y
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Section 5.1
Scientific Notation and Units
Metric Dollars
100 dollars1 hectodollar
1x102
1 dime1 decidollar
1X10-1
1 cent1 centidollar
1X10-2
10 dollars1 dekadollar
1x101
1 dollar1 dollar1x100
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Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Length– Fundamental unit is the meter – 1 meter = 39.37 inches
Who is taller – a woman 5 ft 6 inches or a man 1.62 meters tall?
Comparing English and metric systems
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Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
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Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Volume – Amount of 3-D space occupied by a
substance – Fundamental unit is meter3 (m3)
1 liter = 2.11 Pints
250mL of milk is close to ½ Pint, 1 Pint, 1 Quart, 1 Gallon?
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Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Mass – Quantity of matter in an object – Fundamental unit is kilogram = 2.2 lbs
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Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
How many quarters in a row to make a meter?
What is the weight in kg of a man who weighs 180 lbs?
How many liters in a six-pack of soda cans?