0.9555… as a Fraction

0.9555… (0.95 repeating) as a fraction is 43/45.

How to convert 0.9555… to a fraction

  1. Let x = 0.9555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 95.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 95 − 9, so 90x = 86.
  5. Solve: x = 86/90. The greatest common divisor is 2, so x = 43/45.

Check

Divide 43 by 45 on a calculator: 43 ÷ 45 = 0.9555555556… which matches 0.9555….

Similar repeating decimals

DecimalFraction
0.9333…14/15
0.939393…31/33
0.9444…17/18
0.949494…94/99
0.959595…95/99
0.9666…29/30
0.969696…32/33
0.9777…44/45

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