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Decimal Expanded Form
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Decimal Expanded Form
Aotearoa’s coastal science team is checking measurements before sending a report. Use place value and powers of 10 to decode each decimal. Show powers of 10 in expanded forms; zero-value places may be included or omitted unless the question says otherwise.
Read the place-value pattern
Each step to the right of the decimal point is one tenth of the place before it.
Hundreds
Tens
Ones (10⁰)
Tenths (10⁻¹)
Hundredths (10⁻²)
Thousandths (10⁻³)
1.At a coastal monitoring station, a sensor reads 8.46 °C. What is the value of the digit 4, and which power of 10 names its place?
2.A water sample is recorded as 3.27 L. Choose the correct expanded form using powers of 10.
- 3 × 10⁰ + 2 × 10⁻¹ + 7 × 10⁻²
- 3 × 10¹ + 2 × 10⁰ + 7 × 10⁻¹
- 3 × 10⁰ + 2 × 10⁻² + 7 × 10⁻¹
- 3 + 2 + 7
3.Decode this sensor expression into a decimal: 5 × 10⁰ + 8 × 10⁻¹ + 2 × 10⁻².
4.Write 6.305, a recorded rainfall depth in centimetres, in expanded form using powers of 10. Include every place, even a place with a zero digit.
5.A tide gauge displays 0.074 m. Write this measurement in expanded form using powers of 10. Be careful to keep the zero in the tenths place.
6.One data label has fallen off. The remaining expression is 2 × 10¹ + 4 × 10⁰ + 9 × 10⁻². What decimal should be written on the label?
7.A field note reads 0.608. Write it as a sum of its non-zero digits multiplied by powers of 10.
8.True or false? In the number 12.58, the digit 5 represents 5 × 10⁻¹, and the digit 8 represents 8 × 10⁻².
TrueFalse
9.Mere writes 4.072 as 4 × 10⁰ + 7 × 10⁻² + 2 × 10⁻³. Explain why the hundredths term is 7 × 10⁻², not 7 × 10⁻¹.
10.Challenge: A measurement is 13.406. Write it in expanded form using powers of 10, then state the value of the digit 4.
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