Multiplication and Division:

Multiplication and Division by Powers of 10

A power of 10 is a number that can be written as 10 raised to a power or exponent. \(10^{1}\) = 10, \(10^{2}\) = 100, \(10^{3}\) = 1000, and \(10^{4}\) = 10000 are all examples of powers of 10. Multiplying or dividing by these powers simply requires us to move the decimal place of the number we’re multiplying or dividing. The following video will explain this and show some examples.

Video Source (07:45 mins) | Transcript

Multiplication by a power of 10: move the decimal to the RIGHT the same number of times as the number of 0’s in the power of 10.

Example: 54.2 × 100 = 5420 or 5420.0 The decimal moved two spaces to the right.

Division by a power of 10: move the decimal to the LEFT the same number of times as the number of 0’s in the power of 10.

Example: 5420.0 ÷ 100 = 54.2 The decimal moved two spaces to the left.

Additional Resources

• Khan Academy: Using Exponents with Powers of 10 (05:33 mins, Transcript)
• Khan Academy: Exponents and Powers of 10 Patterns (06:55 mins, Transcript)
• Khan Academy: Multiplying Decimals by Powers of 10 (03:46 mins, Transcript)