11/13 as a Decimal

11/13 as a decimal is 0.846153…, with the 846153 repeating forever (84.62% rounded).

Result

Answer

\frac{11}{13} = \textcolor{#0b5c56}{0.\overline{846153}}

11/13 as a decimal is 0.846153846153… – the digits 846153 repeat forever.

  • Rounded to 2 places: 0.85
  • Rounded to 4 places: 0.8462
  • Percent: 84.6154%

85 of 100 squares ≈ 11/13

Step-by-step solution

The problem

\frac{11}{13}

  1. Divide 11 by 13 (long division). Write down how many times 13 goes in, carry the remainder, add a 0 and divide again. The remainder 11 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part11 ÷ 1301113 × 0 = 0, 11 − 0 = 11
    Decimal place 1110 ÷ 138613 × 8 = 104, 110 − 104 = 6
    Decimal place 260 ÷ 134813 × 4 = 52, 60 − 52 = 8
    Decimal place 380 ÷ 136213 × 6 = 78, 80 − 78 = 2
    Decimal place 420 ÷ 131713 × 1 = 13, 20 − 13 = 7
    Decimal place 570 ÷ 135513 × 5 = 65, 70 − 65 = 5
    Decimal place 650 ÷ 1331113 × 3 = 39, 50 − 39 = 11

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

    = 11 \div 13 = \textcolor{#0b5c56}{0.\overline{846153}}

All the working together

\begin{aligned} &\frac{11}{13} \\[8pt] &= 11 \div 13 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{846153}}\end{aligned}

11/13 in other forms

Decimal0.846153… (the 846153 repeats forever)
Rounded0.85 (2 places), 0.846 (3 places)
Percent≈ 84.62%
Equivalent fractions22/26, 33/39, 44/52, 55/65

Why it repeats

In lowest terms the denominator is 13 = 13. It has the prime factor 13, which does not divide any power of 10, so the long division never ends: the 846153 repeats forever.

Fractions over 13 as decimals

FractionDecimalPercent
1/130.076923…≈ 7.69%
2/130.153846…≈ 15.38%
3/130.230769…≈ 23.08%
4/130.307692…≈ 30.77%
5/130.384615…≈ 38.46%
6/130.461538…≈ 46.15%
7/130.538461…≈ 53.85%
8/130.615384…≈ 61.54%
9/130.692307…≈ 69.23%
10/130.769230…≈ 76.92%
11/130.846153…≈ 84.62%
12/130.923076…≈ 92.31%

Frequently asked questions

What is 11/13 as a decimal?

11/13 as a decimal is 0.846153… (the 846153 repeats forever). Divide 11 by 13 to get it.

What is 11/13 as a percent?

11/13 is ≈ 84.62%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 11/13 a terminating or a repeating decimal?

Repeating – the 846153 repeats forever. In lowest terms the denominator is 13 = 13. It has the prime factor 13, which does not divide any power of 10, so the long division never ends: the 846153 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.