10/11 as a Decimal

10/11 as a decimal is 0.9090…, with the 90 repeating forever (90.91% rounded).

Result

Answer

\frac{10}{11} = \textcolor{#0b5c56}{0.\overline{90}}

10/11 as a decimal is 0.90909090… – the digits 90 repeat forever.

  • Rounded to 2 places: 0.91
  • Rounded to 4 places: 0.9091
  • Percent: 90.9091%

91 of 100 squares ≈ 10/11

Step-by-step solution

The problem

\frac{10}{11}

  1. Divide 10 by 11 (long division). Write down how many times 11 goes in, carry the remainder, add a 0 and divide again. The remainder 10 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part10 ÷ 1101011 × 0 = 0, 10 − 0 = 10
    Decimal place 1100 ÷ 119111 × 9 = 99, 100 − 99 = 1
    Decimal place 210 ÷ 1101011 × 0 = 0, 10 − 0 = 10

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

    = 10 \div 11 = \textcolor{#0b5c56}{0.\overline{90}}

All the working together

\begin{aligned} &\frac{10}{11} \\[8pt] &= 10 \div 11 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{90}}\end{aligned}

10/11 in other forms

Decimal0.9090… (the 90 repeats forever)
Rounded0.91 (2 places), 0.909 (3 places)
Percent≈ 90.91%
Equivalent fractions20/22, 30/33, 40/44, 50/55

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 90 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 10/11 as a decimal?

10/11 as a decimal is 0.9090… (the 90 repeats forever). Divide 10 by 11 to get it.

What is 10/11 as a percent?

10/11 is ≈ 90.91%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 10/11 a terminating or a repeating decimal?

Repeating – the 90 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 90 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.