0.141414… as a Fraction

0.141414… (0.14 repeating) as a fraction is 14/99.

How to convert 0.141414… to a fraction

  1. Let x = 0.141414... (the underlined part, 14, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 14.141414...
  3. Subtract to cancel the repeating tail: 100x − x = 14 − 0, so 99x = 14.
  4. Solve: x = 14/99. The greatest common divisor is 1, so x = 14/99 (already in lowest terms).

Check

Divide 14 by 99 on a calculator: 14 ÷ 99 = 0.1414141414… which matches 0.141414….

Similar repeating decimals

DecimalFraction
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.142142142…142/999
0.142857142857142857…1/7
0.1444…13/90
0.151515…5/33
0.153153153…17/111

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