1.8333… as a Fraction

1.8333… (1.83 repeating) as a fraction is 11/6. As a mixed number that is 1 5/6.

How to convert 1.8333… to a fraction

  1. Let x = 1.8333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 183.333...
  3. Move the decimal point past the non-repeating digits too: 10x = 18.3333...
  4. Subtract to cancel the repeating tail: 100x − 10x = 183 − 18, so 90x = 165.
  5. Solve: x = 165/90. The greatest common divisor is 15, so x = 11/6.

Since 11 is larger than 6, it can also be written as the mixed number 1 5/6.

Check

Divide 11 by 6 on a calculator: 11 ÷ 6 = 1.8333333333… which matches 1.8333….

Similar repeating decimals

DecimalFraction
1.444…13/9
1.555…14/9
1.666…5/3
1.777…16/9
1.888…17/9
2.111…19/9
2.1666…13/6
2.222…20/9

See also: 11/6 as a mixed number.

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