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Place Value Powers Worksheet

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Place Value Powers Worksheet

Show your working where needed. Use powers of 10 to describe the value of each digit.

Place Value and Powers of 10

1.In 63,482, which power of 10 gives the place value of the digit 4?

10⁰
10¹
10²
10³

2.Which expression expands 8,205 using powers of 10?

8 × 10³ + 2 × 10² + 5 × 10⁰
8 × 10² + 2 × 10¹ + 5 × 10⁰
8 × 10⁴ + 2 × 10³ + 5 × 10¹
8 × 10³ + 2 × 10¹ + 5 × 10²

3.Choose the powers-of-10 expression equal to 0.064.

6 × 10⁻¹ + 4 × 10⁻²
6 × 10⁻² + 4 × 10⁻³
6 × 10⁻³ + 4 × 10⁻²
6 × 10² + 4 × 10³

4.For the number 731.58, state the place name and power of 10 for each digit: 7, 3, 5 and 8.

Multiplying and Dividing by Powers of 10

5.Calculate 386 × 10.

6.Calculate 42.73 × 10.

7.Calculate 6,920 ÷ 10.

8.Calculate 5.6 ÷ 10.

9.Describe what happens to the position of every digit when a number is multiplied by 10. Include what happens to the value of the number.

10.A reusable drink bottle costs $4.20. Its price is multiplied by 10. What is the new price, and why might this calculation not describe a realistic shop price?

Expanded Form and Real-World Problems

11.Write 6,041 as a sum of its non-zero digits multiplied by powers of 10.

12.Write 38.27 as a sum of its non-zero digits multiplied by powers of 10.

13.Write 70,306 as a sum of its non-zero digits multiplied by powers of 10.

14.A research boat travels 3.62 × 10² kilometres between two ports. Write the distance in ordinary decimal notation.

15.A town has an estimated population of 2.4 × 10⁵ people. If its population became ten times as large, express the new population using a power of 10 and in ordinary notation.