Multiplying by powers of ten

Follow the following useful and easy shortcuts when multiplying by powers of ten.

Whole numbers multiplied by powers of 10

When multiplying a whole number by a positive power of ten, just count how many zero(s) you have and attached that to the right of the whole number.

Examples:

1) 56 × 10

There is only one zero, so 56 × 10 = 560

2) 45 × 10,000

There are 4 zeros, so 45 × 10000 = 450000

3) 18 × 10,000,000

There are 7 zeros, so 18 × 10,000,000 = 180,000,000

When multiplying a whole number by a negative power of ten (negative exponent), move the decimal point one place to the left for each zero you see before the 1.

Examples:

1) 38 × 0.1

There is only one zero before the 1, so 38 × 0.1 = 3.8

2) 99 × 0.01

There are 2 zeros before the 1, so 99 × 0.01 = 0.99

Decimals multiplied by powers of 10

When multiplying a decimal by a positive power of ten (positive exponent), move the decimal point one place to the right for each zero you see after the 1.

Examples:

1) 0.56 × 10

There is only one zero, so move the decimal point one place to the right.

0.56 × 10 = 5.6

2) 0.56 × 100

There are 2 zeros, so move the decimal point two places to the right.

0.56 × 100 = 56

3) 0.056 × 1000

There are three zeros, so move the decimal point 3 places to the right.

0.056 × 1000 = 56

4) 0.056 × 100,000

0.056 × 100,000 = 0.056 × 1000 × 100 = 56 × 100 = 5600

When multiplying a decimal by a negative power of ten (negative exponent), move the decimal point one place to the left for each zero you see before the 1.

Note that 0.1 = 10-1, 0.01 = 10-2, 0.001 = 10-3, and so forth....

We call 10-1, 10-2, and 10-3 negative powers of 10 because the exponents are negative.

Examples:

1) 56 × 0.1

There is only one zero, so move the decimal point one place to the left.

56 × 0.1 = 5.6

2) 560 × 0.01

There are 2 zeros, so move the decimal point two places to the left.

560 × 0.01 = 5.6

2) 560 × 0.001

There are 3 zeros, so move the decimal point two places to the left.

560 × 0.001 = 0.560

3) 0.56 × 0.1

There is only one zero, so move the decimal point one place to the left.

0.56 × 0.1 = 0.056

4) 0.56 × 0.01

There are 2 zeros, so move the decimal point two places to the left.

0.56 × 0.01 = 0.0056

Any questions about multiplying by powers of ten? Let me know...

Summary showing how multiplying by powers of ten works 

Multiplying by powers of ten

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