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 \times 10 \times 10 \times 10 = 10 000

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

Rules for Powers of Ten

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.

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Activities 1

Activities 2