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Decimal Expanded Form
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Name:Date:
Decimal Expanded Form
Write decimal numbers as sums of digits multiplied by powers of 10. Show your working where useful.
Place
Power of 10
Value of one digit
Ones
10^0
1
Tenths
10^-1
0.1
Hundredths
10^-2
0.01
Thousandths
10^-3
0.001
Powers of ten and place value
1.What is the value of 10^-3?
- 0.1
- 0.01
- 0.001
- 1,000
2.Which decimal is equal to 6 × 10^-2?
- 0.6
- 0.06
- 0.006
- 60
3.Which power of 10 gives the value of one thousandth?
- 10^3
- 10^-1
- 10^-2
- 10^-3
4.Select the expanded form of 0.42.
- 4 × 10^-1 + 2 × 10^-2
- 4 × 10^-2 + 2 × 10^-1
- 4 × 10^1 + 2 × 10^0
- 42 × 10^-3
Write numbers in expanded form
5.Write 6.38 as a sum of its digits multiplied by powers of 10.
6.Write 0.704 as a sum of its non-zero digits multiplied by powers of 10.
7.Write 23.09 as a sum of its non-zero digits multiplied by powers of 10.
8.Complete the place-value expansion: 5.216 = 5 × + 2 × + 1 × + 6 × .
9.Match each power of 10 to its decimal value.
- 10^-1
- 10^-2
- 10^-3
- 10^0
- 1
- 0.01
- 0.1
- 0.001
Use expanded form
10.A ribbon is 2.68 metres long. Write 2.68 in expanded form using powers of 10, then state the length represented by each digit in metres.
11.A book costs $18.45 in New Zealand dollars. Express 18.45 in expanded form using powers of 10. State what the 4 and 5 represent in this price.
12.Find the decimal represented by 4 × 10^0 + 7 × 10^-1 + 2 × 10^-3.
13.Why is a negative power of 10 used for a digit to the right of the decimal point? Give an example using a digit in the hundredths place.
3 printable pages
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