# Multiplying and Dividing Decimals by Powers of Ten

Need some basic practice with decimals first? Changing Decimals to Fractions

In any multiplication problem, the numbers being
multiplied are called the
*factors*.
For example, in the multiplication problem
$\,23.7\times 10\,,$
the factors are
$\,23.7\,$ and $\,10\,.$

*To multiply a decimal by powers of ten*,
you move the decimal point one place
to the right for each factor of ten.

Recall that $\,10^5\,$ is a shorthand for $\,5\,$ factors of $\,10\,$: $\,10^5 = 10\cdot 10\cdot 10\cdot 10\cdot 10\,.$ Similarly, $\,10^n\,$ is a shorthand for $\,n\,$ factors of $\,10\,.$ The $\,\times\,$ symbol is used for multiplication in these problems, because the centered dot is too easily confused with the decimal point.

## Examples

*To divide a decimal by powers of ten*,
you move the decimal point one place to the left
for each factor of ten.

In this web exercise, division is denoted using either the ‘$\,\div\,$’ symbol, or a horizontal fraction bar.

## Examples

Make sure you understand why this works!
For example, when
$\,2.37\,$ is divided by $\,10\,,$ the
$\,2\,$ *ones* should turn into $\,2\,$ *tenths*.
Moving the decimal point one place to the left accomplishes this.

## Practice

Here, you will practice multiplying and dividing decimals
by powers of ten.
Do *not* insert commas in your answers.
That is, type the answer to
$\,631.47\times 10^3\,$ as
$\,631470\,,$
*not*
$\,631{,}470\,.$