0.142142142… as a Fraction

0.142142142… (0.142 repeating) as a fraction is 142/999.

How to convert 0.142142142… to a fraction

  1. Let x = 0.142142142... (the underlined part, 142, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 142.142142142...
  3. Subtract to cancel the repeating tail: 1000x − x = 142 − 0, so 999x = 142.
  4. Solve: x = 142/999. The greatest common divisor is 1, so x = 142/999 (already in lowest terms).

Check

Divide 142 by 999 on a calculator: 142 ÷ 999 = 0.1421421421… which matches 0.142142142….

Similar repeating decimals

DecimalFraction
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.141414…14/99
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.