0.151515… as a Fraction

0.151515… (0.15 repeating) as a fraction is 5/33.

How to convert 0.151515… to a fraction

  1. Let x = 0.151515... (the underlined part, 15, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 15.151515...
  3. Subtract to cancel the repeating tail: 100x − x = 15 − 0, so 99x = 15.
  4. Solve: x = 15/99. The greatest common divisor is 3, so x = 5/33.

Check

Divide 5 by 33 on a calculator: 5 ÷ 33 = 0.1515151515… which matches 0.151515….

Similar repeating decimals

DecimalFraction
0.141414…14/99
0.142142142…142/999
0.142857142857142857…1/7
0.1444…13/90
0.153153153…17/111
0.1555…7/45
0.161616…16/99
0.16333…49/300

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