Multiplying by Powers of Ten

In the base ten number system, it is extremely easy to multiply by powers of ten.
To multiply by $\,10^1 = 10\,$, put $\,1\,$ zero at the end of the number: $237\cdot 10 = 2{,}370\,$
To multiply by $\,10^2 = 100\,$, put $\,2\,$ zeros at the end of the number: $237\cdot 100 = 23{,}700\,$

To multiply by $\,10^n\,$ (which is $\,1\,$ followed by $\,n\,$ zeroes),
put $\,n\,$ zeros at the end of the number.
For example, $\,237 \cdot 10^7 = 2{,}370{,}000{,}000\,$.

Think about why this is so easy!
When, say, $\,237\,$ is multiplied by $\,10\,$:

the $\,2\,$ hundreds become $\,2\,$ thousands;
the $\,3\,$ tens become $\,3\,$ hundreds;
the $\,7\,$ ones become $\,7\,$ tens.

Each digit needs to shift into the next-left place value.
Putting the zero at the end of the number accomplishes this.

In this exercise, multiplication is denoted in two ways:

using a centered dot: $\,237\cdot 10^3\,$
using the ‘times’ symbol: $\,237\times 10^3\,$
This context—multiplying by powers of ten—is one of the only places in algebra and beyond
where use of the ‘$\,\times\,$’ symbol for multiplication is appropriate.
For more information, see Scientific Notation.

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 Fractions

Here, you will practice multiplying by powers of ten.
Do not insert commas in your answers for this web exercise.
That is, type the answer to

$\,631\times 10^3\,$ as $\,631000\,$, not

$\,631{,}000\,$.

(an even number, please)