MULTIPLYING AND DIVIDING DECIMALS BY POWERS OF TEN

In any multiplication problem, the numbers being multiplied are called the factors.
For example, in the multiplication problem $\,23.1\times 10\,$, the factors are $\,23.1\,$ 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.
The $\,\times\,$ symbol is used for multiplication in these problems, because the centered dot is too easily confused with the decimal point.

EXAMPLES:
$23.19 \times 10 = 231.9$
Move the decimal point one place to the right.
$7.001 \times 10^3 = 7001$
Move the decimal point three places to the right.
$0.03 \times 10^4 = 300$
Move the decimal point four places to the right, inserting zeros as needed.

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:
$23.1 \div 10 = 2.31$
Move the decimal point one place to the left.
$\displaystyle\frac{7.001}{10^3} = 0.007001$
Move the decimal point three places to the left, inserting zeros as needed.

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.

Master the ideas from this section

When you're done practicing, move on to:
Changing Decimals to Percents

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