10/13 as a Decimal

10/13 as a decimal is 0.769230…, with the 769230 repeating forever (76.92% rounded).

Result

Answer

\frac{10}{13} = \textcolor{#0b5c56}{0.\overline{769230}}

10/13 as a decimal is 0.769230769230… – the digits 769230 repeat forever.

  • Rounded to 2 places: 0.77
  • Rounded to 4 places: 0.7692
  • Percent: 76.9231%

77 of 100 squares ≈ 10/13

Step-by-step solution

The problem

\frac{10}{13}

  1. Divide 10 by 13 (long division). Write down how many times 13 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 ÷ 1301013 × 0 = 0, 10 − 0 = 10
    Decimal place 1100 ÷ 137913 × 7 = 91, 100 − 91 = 9
    Decimal place 290 ÷ 1361213 × 6 = 78, 90 − 78 = 12
    Decimal place 3120 ÷ 139313 × 9 = 117, 120 − 117 = 3
    Decimal place 430 ÷ 132413 × 2 = 26, 30 − 26 = 4
    Decimal place 540 ÷ 133113 × 3 = 39, 40 − 39 = 1
    Decimal place 610 ÷ 1301013 × 0 = 0, 10 − 0 = 10

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

    = 10 \div 13 = \textcolor{#0b5c56}{0.\overline{769230}}

All the working together

\begin{aligned} &\frac{10}{13} \\[8pt] &= 10 \div 13 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{769230}}\end{aligned}

10/13 in other forms

Decimal0.769230… (the 769230 repeats forever)
Rounded0.77 (2 places), 0.769 (3 places)
Percent≈ 76.92%
Equivalent fractions20/26, 30/39, 40/52, 50/65

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 769230 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 10/13 as a decimal?

10/13 as a decimal is 0.769230… (the 769230 repeats forever). Divide 10 by 13 to get it.

What is 10/13 as a percent?

10/13 is ≈ 76.92%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 10/13 a terminating or a repeating decimal?

Repeating – the 769230 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 769230 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.