0.3555… as a Fraction

0.3555… (0.35 repeating) as a fraction is 16/45.

How to convert 0.3555… to a fraction

  1. Let x = 0.3555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 35.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 35 − 3, so 90x = 32.
  5. Solve: x = 32/90. The greatest common divisor is 2, so x = 16/45.

Check

Divide 16 by 45 on a calculator: 16 ÷ 45 = 0.3555555556… which matches 0.3555….

Similar repeating decimals

DecimalFraction
0.343434…34/99
0.3444…31/90
0.345345345…115/333
0.353535…35/99
0.363636…4/11
0.3666…11/30
0.373737…37/99
0.3777…17/45

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