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## Multiply and Divide by Powers of 10 - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=a

Compute.

 1 `a. 7 × 1,000 = ` `b. 7 × 10,000 = ` `c. 7 × 100,000 = ` 2 `a. 2 × 10,000 = ` `b. 2 × 100,000 = ` `c. 2 × 1,000,000 = `

### Complexity=2, Mode=a

Compute.

 1 `a. 18 × 101 = ` `b. 18 × 102 = ` `c. 18 × 103 = ` 2 `a. 82 × 102 = ` `b. 82 × 103 = ` `c. 82 × 104 = `

### Complexity=1, Mode=b

Compute.

 1 `a. 4.69141 × 100 = ` `b. 4.69141 × 1,000 = ` `c. 4.69141 × 10,000 = ` 2 `a. 4.6631 × 101 = ` `b. 4.6631 × 102 = ` `c. 4.6631 × 103 = `

### Complexity=2, Mode=b

Compute.

 1 `a. 6.24762 × 104 = ` `b. 6.24762 × 105 = ` `c. 6.24762 × 106 = ` 2 `a. 8.6106 × 1,000 = ` `b. 8.6106 × 10,000 = ` `c. 8.6106 × 100,000 = `

### Complexity=1, Mode=c

Compute.

 1 `a. 7,065.6 ÷ 101 = ` `b. 7,065.6 ÷ 102 = ` `c. 7,065.6 ÷ 103 = ` 2 `a. 8,102,318.9 ÷ 104 = ` `b. 8,102,318.9 ÷ 105 = ` `c. 8,102,318.9 ÷ 106 = `

### Complexity=2, Mode=c

Compute.

 1 `a. 34 ÷ 101 = ` `b. 34 ÷ 102 = ` `c. 34 ÷ 103 = ` 2 `a. 61,204.2 ÷ 10,000 = ` `b. 61,204.2 ÷ 100,000 = ` `c. 61,204.2 ÷ 1,000,000 = `

### Complexity=1

Compute.

 1.   `4.84524 × 104 = ` 2.   `521,388.2 ÷ 1,000,000 = `

### Complexity=2

Compute.

 1.   `0.1088 × 100,000 = ` 2.   `80 ÷ 102 = `

### Complexity=1, Mode=a

Compute.

1
`a. 7 × 1,000 = `
`b. 7 × 10,000 = `
`c. 7 × 100,000 = `
Solution
When multiplying a whole number by a power of 10, add the number of zeroes of that power of 10 to the end of the whole number.

Example: 7 × 10,000
10,000 is 1 followed by 4 zeroes.
 7 × 10,000 = 7 followed by 4 zeroes = 70,000
2
`a. 2 × 10,000 = `
`b. 2 × 100,000 = `
`c. 2 × 1,000,000 = `
Solution
When multiplying a whole number by a power of 10, add the number of zeroes of that power of 10 to the end of the whole number.

Example: 2 × 100,000
100,000 is 1 followed by 5 zeroes.
 2 × 100,000 = 2 followed by 5 zeroes = 200,000

### Complexity=2, Mode=a

Compute.

1
`a. 18 × 101 = `
`b. 18 × 102 = `
`c. 18 × 103 = `
Solution
When multiplying a whole number by a power of 10, add the number of zeroes of that power of 10 to the end of the whole number.

Example: 18 × 102
102 is 1 followed by 2 zeroes.
 18 × 102 = 18 followed by 2 zeroes = 1,800
2
`a. 82 × 102 = `
`b. 82 × 103 = `
`c. 82 × 104 = `
Solution
When multiplying a whole number by a power of 10, add the number of zeroes of that power of 10 to the end of the whole number.

Example: 82 × 103
103 is 1 followed by 3 zeroes.
 82 × 103 = 82 followed by 3 zeroes = 82,000

### Complexity=1, Mode=b

Compute.

1
`a. 4.69141 × 100 = `
`b. 4.69141 × 1,000 = `
`c. 4.69141 × 10,000 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 4.69141 × 10,000 10,000 is 1 followed by 4 zeroes. Move the decimal point 4 places to the right. 4.69141 × 10,000 = 46914.1
2
`a. 4.6631 × 101 = `
`b. 4.6631 × 102 = `
`c. 4.6631 × 103 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 4.6631 × 103 103 is 1 followed by 3 zeroes. Move the decimal point 3 places to the right. 4.6631 × 103 = 4663.1

### Complexity=2, Mode=b

Compute.

1
`a. 6.24762 × 104 = `
`b. 6.24762 × 105 = `
`c. 6.24762 × 106 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 6.24762 × 106 106 is 1 followed by 6 zeroes. Move the decimal point 6 places to the right. Add extra zeroes when the decimal point moves beyond the original decimal. 6.24762 × 106 = 6247620
2
`a. 8.6106 × 1,000 = `
`b. 8.6106 × 10,000 = `
`c. 8.6106 × 100,000 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 8.6106 × 100,000 100,000 is 1 followed by 5 zeroes. Move the decimal point 5 places to the right. Add extra zeroes when the decimal point moves beyond the original decimal. 8.6106 × 100,000 = 861060

### Complexity=1, Mode=c

Compute.

1
`a. 7,065.6 ÷ 101 = `
`b. 7,065.6 ÷ 102 = `
`c. 7,065.6 ÷ 103 = `
Solution
When dividing a decimal by a power of 10, move the decimal point to the left by the number of zeroes of the power of 10.

 Example: 7,065.6 ÷ 103 103 is 1 followed by 3 zeroes. Move the decimal point 3 places to the left. 7,065.6 ÷ 103 = 7.0656
2
`a. 8,102,318.9 ÷ 104 = `
`b. 8,102,318.9 ÷ 105 = `
`c. 8,102,318.9 ÷ 106 = `
Solution
When dividing a decimal by a power of 10, move the decimal point to the left by the number of zeroes of the power of 10.

 Example: 8,102,318.9 ÷ 106 106 is 1 followed by 6 zeroes. Move the decimal point 6 places to the left. 8,102,318.9 ÷ 106 = 8.1023189

### Complexity=2, Mode=c

Compute.

1
`a. 34 ÷ 101 = `
`b. 34 ÷ 102 = `
`c. 34 ÷ 103 = `
Solution
When dividing a decimal by a power of 10, move the decimal point to the left by the number of zeroes of the power of 10.

 Example: 34 ÷ 103 103 is 1 followed by 3 zeroes. Move the decimal point 3 places to the left. Add extra zeroes when the decimal point moves beyond the original decimal. 34 ÷ 103 = 0.034
2
`a. 61,204.2 ÷ 10,000 = `
`b. 61,204.2 ÷ 100,000 = `
`c. 61,204.2 ÷ 1,000,000 = `
Solution
When dividing a decimal by a power of 10, move the decimal point to the left by the number of zeroes of the power of 10.

 Example: 61,204.2 ÷ 1,000,000 1,000,000 is 1 followed by 6 zeroes. Move the decimal point 6 places to the left. Add extra zeroes when the decimal point moves beyond the original decimal. 61,204.2 ÷ 1,000,000 = 0.0612042

### Complexity=1

Compute.

1
`4.84524 × 104 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 4.84524 × 104 104 is 1 followed by 4 zeroes. Move the decimal point 4 places to the right. 4.84524 × 104 = 48452.4
2
`521,388.2 ÷ 1,000,000 = `
Solution
When dividing a decimal by a power of 10, move the decimal point to the left by the number of zeroes of the power of 10.

 Example: 521,388.2 ÷ 1,000,000 1,000,000 is 1 followed by 6 zeroes. Move the decimal point 6 places to the left. 521,388.2 ÷ 1,000,000 = 0.5213882

### Complexity=2

Compute.

1
`0.1088 × 100,000 = `
Solution
When multiplying a decimal by a power of 10, move the decimal point to the right by the number of zeroes of the power of 10.

 Example: 0.1088 × 100,000 100,000 is 1 followed by 5 zeroes. Move the decimal point 5 places to the right. Add extra zeroes when the decimal point moves beyond the original decimal. 0.1088 × 100,000 = 10880
`80 ÷ 102 = `   