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#.