# Multiplication and Division by Powers of 10

When you're multiplying or dividing a decimal by a power of 10, there are some nice shortcuts.
First we'll show you how to solve one of these problems without the shortcut. That should heighten your appreciation for it once we tell you about it.

Sample Problem

We then write  as a decimal to get 0.3

That's the long way. Too much work, right? We agree. Couple more examples and then you can start taking the shortcut. Just try not to get your legs cut up in the brambles.

Sample Problem

Sample Problem

Shortcut time. From looking at the above examples we can see that to multiply a decimal by a power of 10, all we do is move the decimal point to the right as many places as there are 0s in that power of 10. Multiplying by 100? Scooch it over two spots. Multiplying by 10,000? Move it over four. Multiplying by 52,398? Move it over... psych. Not in base 10. No shortcut for you.

When dividing a decimal by a power of 10, we move the decimal point to the left instead. As a way to remember this, picture the volume control on your iPod. You rotate it to the right to increase (multiply) the volume, and to the left to decrease (divide) the volume. Or, if it's a decimal that you really, really like, you can always put it on repeat. Like so: 0.33333333...

Here's how it works without the shortcut, in case you care:

Sample Problem