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Maths Quiz - Level 3-4 Numbers - Decimals - Powers of 10 (Questions)

Move decimals using powers of 10. Learn how multiplying or dividing by 10, 100, and 1,000 shifts digits and supports scientific notation.

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Fascinating Fact:

Scientists use powers of 10 to measure distances in space, such as the Earth being about 1.5 × 108 kilometres from the Sun.

In KS3 Maths, powers of 10 help you scale numbers quickly. Multiplying by 10, 100, or 1,000 shifts digits left; dividing shifts them right. You also write very large or small values using scientific notation, like 3.75 × 104 or 6.2 × 10−3.

Key Terms

  • Power of 10: A number like 10, 100, 1,000 or 10n, used to scale values by shifting digits.
  • Scientific notation: Writing a number as a × 10n with 1 ≤ a < 10 and integer n.
  • Place value shift: Moving the decimal point left or right when multiplying or dividing by powers of 10.

Frequently Asked Questions (Click to see answers)

How do powers of 10 move the decimal point?

Multiply by 10, 100, 1,000 to move the decimal right 1, 2, 3 places. Divide to move it left. Example: 3.47 × 100 = 347; 58.2 ÷ 10 = 5.82.

What is scientific notation for decimals?

Write numbers as a × 10n with 1 ≤ a < 10. Examples: 0.0062 = 6.2 × 10−3; 45,000 = 4.5 × 104.

Why does multiplying by 10n change place value?

Each factor of 10 scales a number by one place value. Ten ones make a ten, ten tens make a hundred, so digits shift positions by n places.

Try These Related Quizzes

1. What is 4.65 x 10?
[ ] 0.465
[ ] 46.5
[ ] 465
[ ] 4,650
2. What is 0.08 x 10?
[ ] 0
[ ] 0.1
[ ] 0.8
[ ] 8
3. What is 68.72 / 10?
[ ] 6
[ ] 6.872
[ ] 687.2
[ ] 6,872
4. What is 0.04 / 10?
[ ] 0.004
[ ] 004
[ ] 00.4
[ ] 4
5. What is 7.75 x 100?
[ ] 0.775
[ ] 0.7
[ ] 77.5
[ ] 775
6. What is 44.87 x 100?
[ ] 4.4
[ ] 449
[ ] 4,487
[ ] 4,490
7. What is 692.14 / 100?
[ ] 0.69214
[ ] 6.9214
[ ] 69.214
[ ] 6,921.4
8. What is 88.3 / 100?
[ ] 0.883
[ ] 8.083
[ ] 8.83
[ ] 883
9. When multiplying decimals by 100, how many places do the digits move?
[ ] 0
[ ] 1
[ ] 2
[ ] 3
10. When dividing decimals by 10, how many places do the digits move?
[ ] 0
[ ] 1
[ ] 2
[ ] 3

You can find more about this topic by visiting BBC Bitesize - Decimals

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Maths Quiz - Level 3-4 Numbers - Decimals - Powers of 10 (Answers)
1. What is 4.65 x 10?
[ ] 0.465
[x] 46.5
[ ] 465
[ ] 4,650
Just shift the digits one place to the left
2. What is 0.08 x 10?
[ ] 0
[ ] 0.1
[x] 0.8
[ ] 8
Remember it's the digits that move one place to the left when multiplying by 10
3. What is 68.72 / 10?
[ ] 6
[x] 6.872
[ ] 687.2
[ ] 6,872
Just shift the digits one place to the right
4. What is 0.04 / 10?
[x] 0.004
[ ] 004
[ ] 00.4
[ ] 4
Note that you need to add a zero before the decimal point
5. What is 7.75 x 100?
[ ] 0.775
[ ] 0.7
[ ] 77.5
[x] 775
To multiply by 100 move the digits two places to the left
6. What is 44.87 x 100?
[ ] 4.4
[ ] 449
[x] 4,487
[ ] 4,490
To multiply by 100 move the digits two places to the left
7. What is 692.14 / 100?
[ ] 0.69214
[x] 6.9214
[ ] 69.214
[ ] 6,921.4
To divide by 100 move the digits two places to the right
8. What is 88.3 / 100?
[x] 0.883
[ ] 8.083
[ ] 8.83
[ ] 883
Bear in mind the digits move, not the decimal point
9. When multiplying decimals by 100, how many places do the digits move?
[ ] 0
[ ] 1
[x] 2
[ ] 3
2 zeros before the decimal means move 2 places
10. When dividing decimals by 10, how many places do the digits move?
[ ] 0
[x] 1
[ ] 2
[ ] 3
1 zero means move 1 place
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