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# Powers of Ten

A power of ten is a power where the base is $10$ and the exponent is an integer, like this:

 $1{0}^{n}$

If $n$ is larger than 0, you multiply 10 by itself $n$ times. If $n$ is less than 0, you multiply $\frac{1}{10}$ by itself $n$ times.

Example 1

Find the power $1{0}^{4}$ and write it as an ordinary number

 $1{0}^{4}=10×10×10×10=10\phantom{\rule{0.17em}{0ex}}000$

Example 2

Calculate the power $1{0}^{-3}$ and write it as an ordinary fraction

 $1{0}^{-3}=\frac{1}{1{0}^{3}}=\frac{1}{10×10×10}=\frac{1}{1000}$

Note! In the last example, you can see that the power has a negative exponent $1{0}^{-3}$, and it has changed from being above, to below, the fraction bar. The expression has become $\frac{1}{1{0}^{3}}$. You put 1 in the numerator because you only have one $1{0}^{-3}$.

Rule

### RulesforPowersofTen

When you work with powers of ten it is good to remember that:

• when you multiply by 10, you move the decimal mark one place to the right.

• when you multiply by a power $1{0}^{n}$, you move the decimal mark $n$ places to the right.

• when you divide by 10 (or multiply by $\frac{1}{10}\right)$, you move the decimal mark one place to the left.

• when you multiply by a power $1{0}^{-n}$, you move the decimal mark $n$ places to the left.