Welcome to the Wonderful World of ….
Expectations
- represent, compare, and order wholenumbers to 1 000 000.
– demonstrate an understanding of place value in whole numbers from 0.001 to 1 000 000.
– read and print in words whole numbers to one hundred thousand.
NumeralDigitPlace ValueFace ValueZeroPlace HolderValuePeriodsScientific NotationExpanded FormWritten FormStandard Form
Numerals: A symbol or name that stands for a number.Numerals = Numbers (synonymns) Examples: 3, 49 and twelve are all numerals
Digits: A symbol used to make numerals.
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in everyday numbers.
Example: the numeral 153 is made up of 3 digits ("1", "5" and "3").
Place Value is the value of a digit determined by its position in a number.
A place value chart helps us to read and understand large
numbers.
• In each one of your bags, you have the following place value names. Can you put them in order from smallest to largest?
tens thousandshundreds hundred millionsmillions ten thousandshundred thousands ten millionsones billions
Smallest to Largest»Ones»Tens»Hundreds»Thousands»ten thousand»Hundred thousand»Millions»Ten millions»Hundred millions»Billions
Did you get them all right?
Great Work!
A place value chart helps us to read and understand large
numbers.
Numbers Get Bigger Numbers Get
Smaller
Trillions Billions Millions Thousands
Ones or Units
•
Hundre
d T
rillion
Ten T
rillion
Trillio
n
Hundre
d B
illion
Ten B
illion
Billio
n
Hundre
d M
illion
Ten M
illion
Millio
n
Hundre
d T
housa
nd
Ten T
housa
nd
Thousa
nd
Hundre
d
Ten
One
•
Tenth
s
Hundre
dth
s
Thousa
ndth
s
Ten T
housa
ndth
s
Hundre
d
Thousa
ndth
s
Millio
nth
s
•
•
Trillions Billions Millions Thousands
Ones or Units
•
Hundre
d T
rillion
Ten T
rillion
Trillio
n
Hundre
d B
illion
Ten B
illion
Billio
n
Hundre
d M
illion
Ten M
illion
Millio
n
Hundre
d T
housa
nd
Ten T
housa
nd
Thousa
nd
Hundre
d
Ten
One
•
Tenth
s
Hundre
dth
s
Thousa
ndth
s
Ten T
housa
ndth
s
Hundre
d
Thousa
ndth
s
Millio
nth
s
•
•
Place ValuesPeriod Name
• Each digit in a number has a place value , a face value and a value.
• In the number 4 856, the digit 4 is in the thousands place value.
• Meaning the place value is thousands.
• The number you see (4) is the face value.
4 856
Face value is 4
Place value is
thousands
What is the place value of the six (6) in each of the following numbers?
a) 16 978
thousands
b) 45 678 090
hundred thousandsc) 69
218ten thousandsd) 1 769
e) 92 628f) 978 856
g) 6 876 432
Place Value (?)
tens
hundreds
onesmillions
a. What is the face value of the digit in the hundreds place in each of the following numbers?
a) 16 978
9
b) 45 678 090c) 69 218
0
8
d) 1 769
e) 92 628f) 978 856
g) 6 876 432
Face Value (?)
2
6
4
7
The value of a place is how much the digit in that place is worth.
Example: What is the value of the digit four (4) in each number?
a) 456
c) 567 894
b) 45 678
d) 99 040
a) 400b) 40 000
c) 4
d) 40
a. What is the place value of the nine (9) in each of the following numbers?
b. What is the value of the nine (9) in each of the following numbers
a) 12 978
900hundredsb) 45 678
090tens
c) 79 018
90
thousands
900 000
d) 1 009
e) 92 128f) 978 085
g) 9 876 432
Place Value (?)
Value (?)
9 000
90 000
9 000 000
9ones
ten thousandshundred
thousandsmillions
• Zero is used as a place holder to show there is a place value, but there is no value to that place.
• Zeros are put in to the right of numbers
Example: 40 556
Zero is the place holder for the thousands place because there is no value for it, but we still need to show that there is a place for the thousands
• Numbers are grouped in sets of three called a period.
• Each period has three places: the ones, tens and hundreds.
128 063 245 791
THOUSANDS
MILLIONS
BILLIONS
UNITSones, tens, hundreds
Example4,658,089Millions period
Thousands period
Ones period
Four million, six hundred fifty-eight thousand, eighty-nine.
Hundre
d
Millio
n
Ten
Millio
n
Millio
ns
Hundre
dThousa
nd
Ten T
housa
nd
Thousa
nd
Hundre
d
Ten
One
Tenth
s
Hundre
dth
s
Thousa
ndth
s
1 2 1 5 3 7 6 8 9
Millions ThousandsOnes or Units
1. Read the entire number in each period, then add the period name to the ende.g. “One hundred twenty one” million
“Five hundred thirty seven” thousand“Six hundred eighty nine”
One hundred twenty one million, five hundred thirty seven thousand, six hundred eighty nine.
***Notice no AND was used to read whole numbers***
When saying large numbers you should:
A)start with the largest place value grouping (period) on the left hand side.
B)Say the number, then say the grouped place value period
“Thirty four” + million = “Thirty four million”
34 907 521
34 907 521
C) Move to right and say the number in the next period.
“Nine hundred seven” + thousand = “Nine hundred seven thousand”
D) Keep moving right and say the number in the next period.
“Five hundred twenty one” + hundreds = “Five hundred twenty one”
*** the period name for the hundreds can be dropped when saying or writing the number. ***
34 907 521
34 907 521
34 907 521Now you can add all the names together.
“Thirty-four million nine hundred seven five hundred twenty-one”
ALERTALERT“AND” is only said or written when there is a
decimal. DO NOT say “and” if there isn’t a decimal. ( It’s
hard, but you can do it!)
12 001
1.Say the number in the left period first.2.Next, add the period name to the end of it. 3.Then say the number in the period to its right.4.We can leave the family name hundreds off.
Remember No “and” is used, since we are not using decimals yet.
12 001 = Twelve thousand one
1 000 562
When there is no value in one family, you do not have to include saying that family when writing the number.
Notice we did not include the thousands period. We did not have to include zero thousands
1 000 562 = one million five hundred sixty
two
Five hundred forty six546
8 601
12 897 000
3 010
77
1 000 004 600
155 954 523
13 050
Eight thousand six hundred one
Thirteen thousand fifty
Seventy seven
Three thousand ten
One billion four thousand six hundred
One hundred fifty five million nine hundred fifty four thousand five hundred twenty three
Twelve million eight hundred ninety seven thousand
Six hundred sixty six 666
19 527 000
39
2 000 030 016
341 954 8888
9 001
8 310
20 051
Eight thousand three hundred ten
twenty thousand fifty one
Thirty nine
nine thousand one
Two billion thirty thousand sixteen
Three hundred forty one million nine hundred fifty four thousand eighthundred eighty eight
nineteen million five hundred twenty seven thousand
Write these numbers in words, then try and say them outloud.
a)345b)20c)45 907d)5 678e)7 000f)12 002 g)75 802h)282i)56j)2 450 781
b) Twentyc) Forty Five thousand nine hundred seven
e) Seven thousand
g) Seventy five thousand eight hundred two
f) Twelve thousand two
i) Fifty six
h) Two hundred eighty two
j) Two million four hundred fifty thousand seven hundred eighty one
d) Five thousand six hundred seventy eight
a) Three hundred forty five
When writing a large number put a space between each period
345 905 - Canadian Way
345,905 - American Way
Sometimes you will see a larger numbe written with a comma in between the periods. This is the American way of writing larger numbers
a). 531 b). 1 256c). 72 078
g). 601 345
d). 450 943
f). 72 078
e). 67
h). 3 567 980
i). 13 500 001
Can you say these large numbers out loud?
a). 531 b). 1 256
a). Five hundred thirty one
c). 72 078c). Seventy two thousand seventy eight
g). 601 345
d). 450 943
f). 72 078
e). 67
h). 3 567 980
b). One thousand two hundred fifty six
d). Four hundred fifty thousand nine hundred forty threee). Sixty seven
g). Six hundred one thousand three hundred forty five
f). Seventy two thousand seventy eight
h). Three million five hundred sixty seven thousand nine hundred eighty
i). 13 500 001 h). Thirteen million five hundred one
• When numbers are presented in numerical digits, it is called the standard form of a number.
• a number is written using digits and place value (the regular way to write numbers).
e. g. 4 856 67 1 78 900 679
Standard Forms
• A number is written as a sum using the place and value of each digit.
• This means writing, separately, the value of each digit in the each place value the number.
• The values must be written from largest to smallest, and have an addition sign to shown they are combined
• Zero values are not included.
Method b) 4 x 1000 + 8 x 100 + 5 x 10 + 6 x 1
Method a) 4000 + 800 + 50 + 6
The number 4856 in expanded form is:
You may see expanded form written like this:
Both methods are correct.
The number 5 062 in expanded form is:
5000 + 000 + 60 + 2
** Because there is no value for the hundreds place,we can leave the value of the hundreds place out when writing the expanded form.
5 062 = 5000 + 60 + 2
A trick to writing number in standard form from expanded form is to show the number of lines as there is place values
e.g. Write in standard form 50 000 + 6 000 + 700 + 2
50 000 is the largest of the expanded form shown. So we needFive place value lines
___ ____ ____ ____ _____
The face value of the ten thousands place is 5. Put in 5.
_5__ ____ ____ ____ _____
(Continued) Write in standard form 50 000 + 6 000 + 700 + 2
The face value of the thousands place is 6. Put in 6.
_5__ __6__ ____ ____ _____
The face value of the hundreds place is 7. Put in 7.
_5__ __6__ __7__ ____ _____
The face value of the tens place is 0, because there is no value for the tens place shown. Put in 0.
_5__ __6__ __ 7 _ __0_ _____
The face value of the hundreds place is 2. Put in 2.
_5__ __6__ __7__ __ 0 __ __2__
PracticeWrite the following number in standard form.a)500 + 4b)600 + 70 + 2c)60 000 + 2000 + 900 + 40 + 5d)800 000 + 50 000 + 300 + 60 + 4e)3 x 100 000 + 7 x 10 000 + 2 x 1000 + 8 x 100 + 4 x 10 + 5 x 1f) 6 x 100 000 + 2 x 1000 + 8 x 100 g) 5 x 10 + 6 x 1
602 800
504
850 364
672
62 945
372 845
56
PracticeWrite the following number in expanded form.a)568b)12c)58 900d)123 091e)104 044f) 1 678 932g) 12 456
f) 1 000 000 + 600 000 + 70 000 + 8 000 + 900 + 30 + 2
a) 500 + 60 + 8
d) 100 000 + 20 000 +3 000 + 90 + 1
b) 10 + 2
c) 50 000 + 8 000 + 900
e) 100 000 + 4 000 + 40 + 4
g) 10 000 + 2 000 + 400 + 50 + 6
Standard Form: is the number itself.
e.g. 1; 15,000; 367
Written Form: is the words for the numbers
e.g. one; sixty; twelve million; two hundred eighty thousand ten.
Expanded Form: is writing a number by separating it into each of its place values.
Two Versions:
a). 789 123 = (7 x 100 000) + (8 x 10 000) + (9 x 1 000) + (1 x 100) + (2 x 10) + (3 x 1)
b) 789 123 = 700 000 + 80 000 + 9 000 + 100 + 20 + 3
StandardForm
ExpandedForm
Written Form
10 589 (1 x 10 000) + (5 x 100) + (8 x 10) + (9 x 1) Ten thousand five hundred eighty nine
7 589 588
(7 x 1 000 000) + (5 x 100 000) + (8 x 10 000) + (9 x 1 000) + (5 x 100) + (8 x 10) + (8 x 1)
Seven million five hundred eighty nine thousand five hundred eighty
eight
12.078 (1 x 10) + (2 x 1) + (7 x 0.01) + (8 x 0.001) Twelve AND seventy eight thousandths
0.54669 (5 x 0.1) + (4 x 0.01) + (6 x 0.001) + (6 x 0.0001) + (9 x 0.00001)
Fifty four thousand six hundred sixty nine hundred thousandths
PracticeWrite the following number in standard, expanded and written form.a)234
b)3 405
c)561 783
d)1 876 980
Practice
a) 234 – 234 - 200 + 30 + 4 - two hundred thirty four
b) 3 405 – 3 405 - 3000 + 400 + 5 - threee thousand four hundred five
c) 561 783 – 561 783 - 500 000 + 60 000 + 1 000 + 700 + 80 + 3 - five hundred sixty one thousand seven hundred
eighty three.
Write the following number in standard, expanded and written form.
Practiced) 1 876 980 – 1 876 980 - 1 000 000 + 800 000 + 70 000 + 6 000 + 900 + 80 - one million eight hundred seventy six thousand nine hundred eighty
Representing NumbersHow many ways can you think of to represent
the value of a number?
- Standard form (numbers)
- Written form (words)
- Expanded form (values)- Scientific Notation (values)
- Money (values)
Can you think of any other ways to show the value of a number?
What about …..
Remember the Base 10 System?
= 100
= 10
= 10
= 1 000
** USE A RULER TO DRAW YOUR PICTURES
Representing a Number Using Base 10
E.g. Using diagrams show the value of 2 322
1 000 + 1 000 + 100 + 100 + 100 + 10 + 10 + 1 + 1
= 2 322
PracticeUsing the following pictures, write the following numbers in standard form.
a)
b)
c)
d)
1 111
425
332
3 150
ProblemUsing four different methods represent the value of the
number 3 451.
1. Pictures
3. Written Form
Three thousand four hundred fifty one
4. Scientific Notation
3 x 103 + 4 x 102 + 5 x 101 + 1 x 100
2. Expanded Form
3000 + 400 + 50 + 1
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