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Decimals and Negative Exponents
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Decimals and Negative Exponents
A science team at an airport is checking tiny particles in an air filter. Help Aisha and Finn convert between powers of 10 and decimals. Remember: each step down in the exponent divides by 10.
Read the scale
Use the number line to see how the values get smaller as the exponent decreases.
1.Complete the number line labels: what decimal belongs at the mark for 10⁻²?
2.A filter catches a particle measured at 6 × 10⁻⁵ m. Write its measurement as a decimal in metres.
3.Which expression is equal to 0.0004? Choose one.
- 4 × 10⁻³
- 4 × 10⁻⁴
- 4 × 10⁴
- 40 × 10⁻⁴
4.Tick every expression that has the value 0.001.
- 10⁻³
- 1 ÷ 10³
- 10³
- 1/100
Convert and compare
Show your working where you can. Keep track of the units.
5.A fibre is 0.00008 m long. Write this measurement using a power of 10 in the form 8 × 10ⁿ m. What is n?
6.Match each measurement to its decimal form: 3 × 10⁻⁴ m; 7 × 10⁻⁶ m; 2 × 10⁻³ m. Decimal forms: 0.000007 m, 0.002 m, 0.0003 m.
- 3 × 10⁻⁴ m
- 7 × 10⁻⁶ m
- 2 × 10⁻³ m
- 0.000007 m
- 0.0003 m
- 0.002 m
7.A tiny sensor part measures 0.00025 m. Convert this length to millimetres. (1 m = 1000 mm.)
8.A particle is 1.2 × 10⁻⁷ m wide. Finn says this is 0.00000012 m. Is Finn correct? Explain how the exponent tells you where the decimal point goes.
9.Complete the pattern: 10⁻¹ = , 10⁻² = , 10⁻³ = . What happens to the decimal value each time the exponent decreases by 1?
10.Challenge: a coating is 2.5 × 10⁻⁶ m thick. What is the combined thickness of 1000 identical layers, first in metres and then in millimetres? Use 1 m = 1000 mm.
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