0.2888… as a Fraction

0.2888… (0.28 repeating) as a fraction is 13/45.

How to convert 0.2888… to a fraction

  1. Let x = 0.2888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 28.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 28 − 2, so 90x = 26.
  5. Solve: x = 26/90. The greatest common divisor is 2, so x = 13/45.

Check

Divide 13 by 45 on a calculator: 13 ÷ 45 = 0.2888888889… which matches 0.2888….

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