9/11 as a Decimal

9/11 as a decimal is 0.8181…, with the 81 repeating forever (81.82% rounded).

Result

Answer

\frac{9}{11} = \textcolor{#0b5c56}{0.\overline{81}}

9/11 as a decimal is 0.81818181… – the digits 81 repeat forever.

  • Rounded to 2 places: 0.82
  • Rounded to 4 places: 0.8182
  • Percent: 81.8182%

82 of 100 squares ≈ 9/11

Step-by-step solution

The problem

\frac{9}{11}

  1. Divide 9 by 11 (long division). Write down how many times 11 goes in, carry the remainder, add a 0 and divide again. The remainder 9 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part9 ÷ 110911 × 0 = 0, 9 − 0 = 9
    Decimal place 190 ÷ 118211 × 8 = 88, 90 − 88 = 2
    Decimal place 220 ÷ 111911 × 1 = 11, 20 − 11 = 9

  2. Read off the decimal. A bar over digits means they repeat forever.

    = 9 \div 11 = \textcolor{#0b5c56}{0.\overline{81}}

All the working together

\begin{aligned} &\frac{9}{11} \\[8pt] &= 9 \div 11 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{81}}\end{aligned}

9/11 in other forms

Decimal0.8181… (the 81 repeats forever)
Rounded0.82 (2 places), 0.818 (3 places)
Percent≈ 81.82%
Equivalent fractions18/22, 27/33, 36/44, 45/55

Why it repeats

In lowest terms the denominator is 11 = 11. It has the prime factor 11, which does not divide any power of 10, so the long division never ends: the 81 repeats forever.

Fractions over 11 as decimals

FractionDecimalPercent
1/110.0909…≈ 9.09%
2/110.1818…≈ 18.18%
3/110.2727…≈ 27.27%
4/110.3636…≈ 36.36%
5/110.4545…≈ 45.45%
6/110.5454…≈ 54.55%
7/110.6363…≈ 63.64%
8/110.7272…≈ 72.73%
9/110.8181…≈ 81.82%
10/110.9090…≈ 90.91%

Frequently asked questions

What is 9/11 as a decimal?

9/11 as a decimal is 0.8181… (the 81 repeats forever). Divide 9 by 11 to get it.

What is 9/11 as a percent?

9/11 is ≈ 81.82%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 9/11 a terminating or a repeating decimal?

Repeating – the 81 repeats forever. In lowest terms the denominator is 11 = 11. It has the prime factor 11, which does not divide any power of 10, so the long division never ends: the 81 repeats forever.

More fractions as decimals

Any other fraction: use the Fraction to Decimal Calculator, or see every fraction to sixteenths on the printable fraction chart.