Powers of 10: Multiplying and Dividing Worksheet

Question 1

Find the product: 47 × 10. Explain what happens to the value of each digit.

Accepted Answer

47 × 10 = 470. Each digit moves one place to the left, so the number becomes 10 times as large.

Question 2

Find the quotient: 6,300 ÷ 100. Explain your answer.

Accepted Answer

6,300 ÷ 100 = 63. Dividing by 100 moves each digit two places to the right, so the number becomes one hundredth as large.

Question 3

Complete the pattern: 8, 80, 800, 8,000, _____.

Accepted Answer

The next number is 80,000. Each number is multiplied by 10 to get the next number in the pattern.

Question 4

Use place value to solve: 3.6 × 100.

Accepted Answer

3.6 × 100 = 360. The digits move two places to the left because 100 has two zeros.

Question 5

Use place value to solve: 540 ÷ 10.

Accepted Answer

540 ÷ 10 = 54. The digits move one place to the right because the number is divided by 10.

Question 6

A school orders 25 boxes of pencils. Each box has 100 pencils. How many pencils does the school order in all?

Accepted Answer

The school orders 2,500 pencils in all because 25 × 100 = 2,500.

Question 7

A baker has 4,800 cookies and packs them equally into boxes of 100 cookies. How many full boxes can the baker pack?

Accepted Answer

The baker can pack 48 full boxes because 4,800 ÷ 100 = 48.

Question 8

Fill in the missing number: 72 × _____ = 72,000.

Accepted Answer

The missing number is 1,000 because 72 × 1,000 = 72,000.

Question 9

Fill in the missing number: 9,500 ÷ _____ = 95.

Accepted Answer

The missing number is 100 because 9,500 ÷ 100 = 95.

Question 10

Complete the table for multiplying by powers of 10: 14 × 10 = _____, 14 × 100 = _____, and 14 × 1,000 = _____.

Accepted Answer

14 × 10 = 140, 14 × 100 = 1,400, and 14 × 1,000 = 14,000. Each larger power of 10 moves the digits one more place to the left.

Question 11

Find the quotient: 7.2 ÷ 10.

Accepted Answer

7.2 ÷ 10 = 0.72. Dividing by 10 moves the digits one place to the right in the place value chart.

Question 12

Which expression has the greatest value: 56 × 10, 56 × 100, or 56 × 1,000? Explain.

Accepted Answer

56 × 1,000 has the greatest value because multiplying by 1,000 makes 56 larger than multiplying by 10 or 100.

Question 13

A runner tracks distances in meters. One kilometer is 1,000 meters. How many meters are in 6 kilometers?

Accepted Answer

There are 6,000 meters in 6 kilometers because 6 × 1,000 = 6,000.

Question 14

A bottle holds 2,000 milliliters of water. If each cup holds 100 milliliters, how many cups can be filled?

Accepted Answer

20 cups can be filled because 2,000 ÷ 100 = 20.

Question 15

Explain the error: A student says 4.5 × 100 = 45. What is the correct answer?

Accepted Answer

The correct answer is 450. The student only moved the digits one place, but multiplying by 100 moves the digits two places to the left.

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