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Skillsheet
Place value
The position of a digit in a number shows its value. This is called place value.
For example, in the number 21 054 937:
Ten
Hundred
Ten
millions
Millions
thousands
thousands
Thousands
Hundreds
2
1
0
5
4
9
Tens
3
Units
7
7 is in the units column and has a value of 7 (7 units).
3 is in the tens column and has a value of 30 (3 tens).
9 is in the hundreds column and has a value of 900 (9 hundreds).
4 is in the thousands column and has a value of 4000 (4 thousands).
5 is in the ten thousands column and has a value of 50 000 (5 ten thousands).
0 is in the hundred thousands column and has a value of 0 (0 hundred thousands).
1 is in the millions column and has a value of 1 000 000 (1 million).
2 is in the ten millions column and has a value of 20 000 000 (2 ten millions).
Example 1
In the number 147 516:
a write the value of 5
b write the digit in the ten thousands place.
Solution
a The value of 5 is 500.
b The digit in the ten thousands place is 4.
Expanded notation
By writing a number in expanded notation, we show the place value of every digit in the number.
Example 2
Write 986 480 in expanded notation.
Solution
986 480 ¼ 900 000 þ 80 000 þ 6000 þ 400 þ 80 þ 0
¼ 9 100 000 þ 8 10 000 þ 6 1000 þ 4 100 þ 8 10 þ 0 1
This can also be written in a shorter way using powers of 10:
986 480 ¼ 9 105 þ 8 104 þ 6 103 þ 4 102 þ 8 10 þ 0 1
Exercise
1 In the number 58 410 729, write the value of:
a 1
b 2
c 4
d 5
e 7
f 8
g 9
h 0
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10011
Number and Algebra: Number and place value
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2 In the number 81 237 596, write the digit in the:
a millions place
b tens place
c ten thousands place
d units place
e hundred thousands place
f hundreds place
g ten millions place
h thousands place
3 What is the place value of the 7 in each number?
a 45 780
b 213 897
c 67 449
d 1 933 517
e 26 175
f 73 240 616
g 175 832
h 37 842 001
c 1 458 617
d 344 820
4 Write each number in expanded notation.
a 7942
b 23 906
5 Write each of these as a single number.
a 4 10 000 þ 9 1000 þ 1 100 þ 2 10 þ 0 1
b 8 1 000 000 þ 2 100 000 þ 5 10 000 þ 3 1000 þ 2 100 þ 7 10 þ 6 1
c 6 100 000 þ 6 10000 þ 4 1000 þ 9 100 þ 5 10 þ 8 1
d 2 104 þ 8 103 þ 6 102 þ 1 10 þ 3 1
e 1 107 þ 5 106 þ 0 105 þ 3 104 þ 6 103 þ 2 102 þ 8 10 þ 4 1
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10011
Number and Algebra: Number and place value
www.nelsonnet.com.au
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Answers
1 a 10 000
b 20
c 400 000
d 50 000 000
f 8 000 000
g 9 (units)
h 0 thousands
2 a 1
b 9
c 3
d 6
e 2
f 5
g 8
h 7
b 7
c 7000
d 7
f 70 000 000
g 70 000
h 7 000 000
e 700
3 a 700
e 70
4 a 7 1000 þ 9 100 þ 4 10 þ 2 1 or 7 103 þ 9 102 þ 4 10 þ 2 1
b 2 10 000 þ 3 1000 þ 9 100 þ 0 10 þ 6 1 or 2 104 þ 3 103 þ 9 102 þ 0 10 þ 6 1
c 1 1 000 000 þ 4 100 000 þ 5 10 000 þ 8 1000 þ 6 100 þ 1 10 þ 7 1 or 1 106 þ 4 105 þ
5 104 þ 8 103 þ 6 102 þ 1 10 þ 7 1
d 3 100 000 þ 4 10 000 þ 4 1000 þ 8 100 þ 2 10 þ 0 1 or 3 105 þ 4 104 þ 4 103 þ 8 102 þ 2 10 þ 0 1
5 a 49 120
b 8 253 276
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10011
c 664 958
d 28 613
Number and Algebra: Number and place value
e 15 036 284
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