# How do you multiply repeating decimals?

May 9, 2018

Round them or use fractions. See explanation.

#### Explanation:

There are really only two ways to multiply repeating decimals: you can round the decimal or use a fractional value of the decimal.

For example:

To multiply $0. \overline{6}$ by $0. \overline{1}$, you can use one of two methods:

Round them:

$0.666666666$ will round to $0.667$, if we use three decimal places, and $0.111111111$ will round to $0.111$.

Multiplying $0.667 \cdot 0.111 = 0.074$

Use fractions:

$0. \overline{6} = \frac{2}{3}$, and $0. \overline{1} = \frac{1}{9}$

Multiplying $\frac{2}{3} \cdot \frac{1}{9} = \frac{2}{27}$, which, converted to a decimal, is also $0.074$.