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 [beautiful math coming... please be patient] $\,23.1\times 10\,$, the factors are [beautiful math coming... please be patient] $\,23.1\,$ 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 [beautiful math coming... please be patient] $\,\times\,$ symbol is used for multiplication in these problems, because the centered dot is too easily confused with the decimal point.

EXAMPLES:
[beautiful math coming... please be patient] $23.19 \times 10 = 231.9$
Move the decimal point one place to the right.
[beautiful math coming... please be patient] $7.001 \times 10^3 = 7001$
Move the decimal point three places to the right.
[beautiful math coming... please be patient] $0.03 \times 10^4 = 300$
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 ‘[beautiful math coming... please be patient] $\,\div\,$’ symbol, or a horizontal fraction bar.

EXAMPLES:
[beautiful math coming... please be patient] $23.1 \div 10 = 2.31$
Move the decimal point one place to the left.
[beautiful math coming... please be patient] $\displaystyle\frac{7.001}{10^3} = 0.007001$
Move the decimal point three places to the left, inserting zeros as needed.

Make sure you understand why this works!
For example, when [beautiful math coming... please be patient] $\,2.37\,$ is divided by $\,10\,$, the [beautiful math coming... please be patient] $\,2\,$ ones should turn into $\,2\,$ tenths.
Moving the decimal point one place to the left accomplishes this.

Master the ideas from this section
by practicing the exercise at the bottom of this page.

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

 
 

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   [beautiful math coming... please be patient] $\,631.47\times 10^3\,$   as   [beautiful math coming... please be patient] $\,631470\,$,   not   [beautiful math coming... please be patient] $\,631{,}470\,$.

Multiply/Divide:
    
(an even number, please)