Multiply by Powers of Ten

Multiplying by powers of ten

When you multiply a number by a power of ten, you are scaling it by 10, 100, 1,000, and so on. The main idea is that each factor of 10 shifts the digits one place to the left.

1) Recognize the power of ten

• (10^1 = 10)
• (10^2 = 100)
• (10^3 = 1{,}000)

So multiplying by (10^n) means moving the decimal point n places to the right.

2) Move the decimal correctly

• If the number is a whole number, you can think of adding zeros.
• If the number has a decimal, shift it right.
• If there are not enough digits, add zeros as needed.

Examples:

• (4.7 \times 10 = 47)
• (4.7 \times 100 = 470)
• (0.36 \times 1{,}000 = 360)

3) Keep the value exact

Write the answer in simplest exact form. Do not round.

4) Check your answer

A quick check is to divide the result by the same power of ten. You should get back the original number.

Example check: (47 \div 10 = 4.7), so (4.7 \times 10 = 47) is correct.

Common mistake to avoid

Do not move digits the wrong way. Multiplying by powers of ten moves the decimal right, not left.