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# Multiplication and Division by Powers of 10

When you're multiplying or dividing a decimal by a power of 10, there are some sweet, sweet 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

Transform both decimals into fractions, then multiply 'em together. 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

Same deal here. We transform 0.4 into a fraction with 10 in the denominator, then multiply by 1000. That'll give us 4000 in the numerator and 10 in the denominator, which reduces to a nice, even 400.

### Sample Problem

Shortcut time. 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 zeros 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...

### Sample Problem

What's 0.6 ÷100?

Let's bust out that shortcut. Since we're dividing by 100, we just slide our decimal point over two spots to the left, since 100 has two zeros.

0.6 ÷100 = 0.006

Here's how it works without the shortcut, just to prove this thing works: