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What is 0.90 repeating as a fraction?

0.9090…=

0.90 repeating as a fraction is 10/11 — exactly, not rounded. As a percent it is ≈ 90.91%.

Improper fraction 10/11Percent ≈ 90.91%Before simplifying 90/99

How to convert 0.9090… to a fraction

  1. Let x = 0.9090… The repeating block "90" has 2 digits.
  2. Multiply by 10^2 and by 10^0 so the repeating tails line up, then subtract.
    100x − 1x = 90 − 0
  3. That gives 99x = 90, so x = 90/99.
  4. Simplify by dividing top and bottom by the GCF, 9.
    90/99 = 10/11

Fractions equal to 10/11

20/22 = 30/33 = 40/44 = 50/55 = 100/110 = 10/11. All are equivalent; 10/11 is the one in lowest terms.

Convert another value with the decimal to fraction converter, see neighbours in the fraction chart, or browse every decimal we list.

Questions people ask

What is 0.90 repeating as a fraction?

0.9090… (0.90 repeating) is exactly 10/11. A repeating decimal is never "about" a fraction: the repeating digits make it equal to 10/11 exactly.

How do you turn 0.90 repeating into a fraction?

Call the number x, multiply it by a power of 10 so the repeating tails line up, and subtract. The tails cancel, leaving 90/99, which simplifies to 10/11.

What is 0.90 repeating as a percent?

10/11 × 100 ≈ 90.91% (the digits keep repeating, so this is rounded to 2 places).