How do you write .888888 (.8 repeating) as a fraction?

2 Answers
Jun 5, 2018

The fraction is #=8/9

Explanation:

Let #X=0.8888888.....#

Then,

#10X=8.8888888.....#

So,

#10X-X=8.8888888..-0.88888888...=8#

#9X=8#

#X=8/9#

Jun 5, 2018

You would write it as #8/9#

Explanation:

If something (a number or pattern) in a decimal is repeating, then you can put it in fraction form like this.

First, identify the repeating pattern or number. For example, in

#34.879879879...#

the pattern is #879#. Or in

#.888888...#

the pattern is #8#.

Next, identify how many digits are in the number. For example, in

#34.879879879...#

there are three digits in the pattern #879#. Also, in

#.888888...#

there is one digit in the pattern #8#.

Lastly, you put the number of pattern digits as the number of nines for the denominator, and you put the pattern as the numerator. For example, in

#34.879879879...#

the fraction form is

#34 879/999#

Also, for

#.888888...#

the proper fraction form would be:

#8/9#