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
$$1{0}^{4}=10\times 10\times 10\times 10=10\phantom{\rule{0.17em}{0ex}}000$$ |
Example 2
Calculate the power $1{0}^{-3}$ and write it as an ordinary fraction
$$1{0}^{-3}=\frac{1}{1{0}^{3}}=\frac{1}{10\times 10\times 10}=\frac{1}{1000}$$ |
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
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 $\frac{1}{10})$, 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.