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# What is 0.78 repeating as a fraction in simplest form?

Updated: 4/28/2022 Wiki User

11y ago Verified answer

Do you mean (a) 0.78888888... or (b) 0.7878787878...?

You can work this out on a calculator, a graphing calculator makes it easier to see.

If your calculator has a button that says [->Frac] or [D->F], the calculator will give you the answer right away. Otherwise, here is a way to do it yourself:

(a) Let x = 0.78888888... Since there is 1 digit that repeats, multiply by 10:

10x = 7.888888..

Now subtract :

10x-9x = 7.888888... - 0.7888888... {just put the '8' into the calculator about 10 times}

9x = 7.1

x = 7.1/9 = 71/90

Check: 71/90 = 0.788888888...

(b) Let x = 0.7878787878 ... Since 2 digits repeat, multiply by 100:

100x = 78.78787878...

100x - x = 78.78787878... - 0.7878787878...

99x = 78

x=78/99

Check: 78/99 = 0.7878787878... Wiki User

11y ago   Cameron Bedford

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