7.888… as a Fraction

7.888… (7.8 repeating) as a fraction is 71/9. As a mixed number that is 7 8/9.

How to convert 7.888… to a fraction

1. Let x = 7.888... (the underlined part, 8, repeats forever).
2. Move the decimal point past one full repeating block: 10x = 78.888...
3. Subtract to cancel the repeating tail: 10x − x = 78 − 7, so 9x = 71.
4. Solve: x = 71/9. The greatest common divisor is 1, so x = 71/9 (already in lowest terms).

Since 71 is larger than 9, it can also be written as the mixed number 7 8/9.

Check

Divide 71 by 9 on a calculator: 71 ÷ 9 = 7.8888888889… which matches 7.888….

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