0.16333… as a Fraction

0.16333… (0.163 repeating) as a fraction is 49/300.

How to convert 0.16333… to a fraction

  1. Let x = 0.16333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 163.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 16.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 163 − 16, so 900x = 147.
  5. Solve: x = 147/900. The greatest common divisor is 3, so x = 49/300.

Check

Divide 49 by 300 on a calculator: 49 ÷ 300 = 0.1633333333… which matches 0.16333….

Similar repeating decimals

DecimalFraction
0.151515…5/33
0.153153153…17/111
0.1555…7/45
0.161616…16/99
0.1666…1/6
0.16666…1/6
0.171717…17/99
0.1777…8/45

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