0.161616… as a Fraction

0.161616… (0.16 repeating) as a fraction is 16/99.

How to convert 0.161616… to a fraction

  1. Let x = 0.161616... (the underlined part, 16, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 16.161616...
  3. Subtract to cancel the repeating tail: 100x − x = 16 − 0, so 99x = 16.
  4. Solve: x = 16/99. The greatest common divisor is 1, so x = 16/99 (already in lowest terms).

Check

Divide 16 by 99 on a calculator: 16 ÷ 99 = 0.1616161616… which matches 0.161616….

Similar repeating decimals

DecimalFraction
0.151515…5/33
0.153153153…17/111
0.1555…7/45
0.16333…49/300
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.