How do you multiply repeating decimals?

1 Answer
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.bar6 by 0.bar1, 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*0.111=0.074

Use fractions:

0.bar6=2/3, and 0.bar1=1/9

Multiplying 2/3*1/9=2/27, which, converted to a decimal, is also 0.074.