Decimals and percentages · Ages 10–11

Powers of 10 worksheet

Part of: Multiplying decimals

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Decimals and percentages · Ages 10–11

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

13.A box holds 10² paper clips. Tsz-ching buys 24 boxes. How many paper clips is that?
Working:
Answer:
14.A cargo ship sails into Victoria Harbour carrying 7.1 × 10³ kg of goods. How many kilograms is that?
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Answer:
15.1 km = 10³ m. Tsz-hin walks 3.2 km from home to the MTR station. How many metres is that?
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Answer:
16.1 m = 10² cm. A rope is 6.25 m long. How many centimetres is that?
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Answer:
17.A computer does 10⁴ sums a second. How many does it do in 28 seconds?
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Answer:
18.A box holds 10² paper clips. Tsz-hin buys 25 boxes. How many paper clips is that?
Working:
Answer:

Show the answers and working

Powers of 10 worksheet: Answers and working

1. 6500
10² is two 10s multiplied. Work out what 10² is, then multiply 65 by it.
10² = 100: 65 × 100 = 6500, two 0s on the end.
2. 8000
10² is two 10s multiplied. Work out what 10² is, then multiply 80 by it.
10² = 100: 80 × 100 = 8000, two 0s on the end.
3. 3100
10³ is three 10s multiplied. When you multiply 3.1 by it, how many places right does the point move?
10³ = 1000: the point moves three places right, with 0s to fill: 3.1 × 1000 = 3100.
4. 6900
10³ is three 10s multiplied. When you multiply 6.9 by it, how many places right does the point move?
10³ = 1000: the point moves three places right, with 0s to fill: 6.9 × 1000 = 6900.
5. 10000, 47000
Count how many 10s are multiplied: that is how many 0s follow the 1.
For 4.7 × 10⁴, how many places right does the point move?
Four 10s multiplied make 10000, 1 and four 0s; 4.7 × 10000 moves the point four places right: 47000.
6. 4.4
10² is 100. Think backwards: what times 100 makes 440?
10² = 100. Think backwards: 440 ÷ 100 = 4.4, the point two places left.
7. 10000, 77000
Count how many 10s are multiplied: that is how many 0s follow the 1.
For 7.7 × 10⁴, how many places right does the point move?
Four 10s multiplied make 10000, 1 and four 0s; 7.7 × 10000 moves the point four places right: 77000.
8. 7.8
10² is 100. Think backwards: what times 100 makes 780?
10² = 100. Think backwards: 780 ÷ 100 = 7.8, the point two places left.

9. D. 10²
The small number on the 10 says how many 10s are multiplied. How many 10s multiply to make 100?
Count the 0s after the 1 in 100: that is the small number on the 10.
10. False
First be sure what 10³ is: 10 × 3, or three 10s multiplied? Work out 88 × 10³, then compare with 2640.
10³ = 10 × 10 × 10 = 1000, not 30: 88 × 1000 = 88000.
11. D. 90 × 1000
10³ is not 10 × 3. Write out what 10³ is, then see which option is 90 times that.
10³ = 10 × 10 × 10 = 1000, so 90 × 10³ = 90 × 1000.
12. A. 15 × 1000
10³ is not 10 × 3. Write out what 10³ is, then see which option is 15 times that.
10³ = 10 × 10 × 10 = 1000, so 15 × 10³ = 15 × 1000.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 2400 paper clips
That is 24 lots of 10². Work out what 10² is first.
10² = 100: 24 × 100 = 2400.
14. 7100 kg
10³ is three 10s multiplied. When you multiply by it, how many places right does the point in 7.1 move?
10³ = 1000: 7.1 × 1000 = 7100.
15. 3200 m
Kilometres to metres is × 10³. How many places right does the point in 3.2 move?
3.2 × 10³ = 3.2 × 1000 = 3200: the point moves three places right.
16. 625 cm
Metres to centimetres is × 10², which is 100. How many places right does the point in 6.25 move?
6.25 × 10² = 6.25 × 100 = 625: the point moves two places right.
17. 280000 sums
28 seconds is 28 lots of 10⁴. How many 0s follow the 1 in 10⁴?
10⁴ = 10000: 28 × 10000 = 280000.
18. 2500 paper clips
That is 25 lots of 10². Work out what 10² is first.
10² = 100: 25 × 100 = 2500.

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