8.111… as a Fraction

8.111… (8.1 repeating) as a fraction is 73/9. As a mixed number that is 8 1/9.

How to convert 8.111… to a fraction

1. Let x = 8.111... (the underlined part, 1, repeats forever).
2. Move the decimal point past one full repeating block: 10x = 81.111...
3. Subtract to cancel the repeating tail: 10x − x = 81 − 8, so 9x = 73.
4. Solve: x = 73/9. The greatest common divisor is 1, so x = 73/9 (already in lowest terms).

Since 73 is larger than 9, it can also be written as the mixed number 8 1/9.

Check

Divide 73 by 9 on a calculator: 73 ÷ 9 = 8.1111111111… which matches 8.111….

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Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.