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