3/13 as a Decimal

3/13 as a decimal is 0.230769…, with the 230769 repeating forever (23.08% rounded).

Result

Answer

\frac{3}{13} = \textcolor{#0b5c56}{0.\overline{230769}}

3/13 as a decimal is 0.230769230769… – the digits 230769 repeat forever.

  • Rounded to 2 places: 0.23
  • Rounded to 4 places: 0.2308
  • Percent: 23.0769%

23 of 100 squares ≈ 3/13

Step-by-step solution

The problem

\frac{3}{13}

  1. Divide 3 by 13 (long division). Write down how many times 13 goes in, carry the remainder, add a 0 and divide again. The remainder 3 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part3 ÷ 130313 × 0 = 0, 3 − 0 = 3
    Decimal place 130 ÷ 132413 × 2 = 26, 30 − 26 = 4
    Decimal place 240 ÷ 133113 × 3 = 39, 40 − 39 = 1
    Decimal place 310 ÷ 1301013 × 0 = 0, 10 − 0 = 10
    Decimal place 4100 ÷ 137913 × 7 = 91, 100 − 91 = 9
    Decimal place 590 ÷ 1361213 × 6 = 78, 90 − 78 = 12
    Decimal place 6120 ÷ 139313 × 9 = 117, 120 − 117 = 3

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

    = 3 \div 13 = \textcolor{#0b5c56}{0.\overline{230769}}

All the working together

\begin{aligned} &\frac{3}{13} \\[8pt] &= 3 \div 13 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{230769}}\end{aligned}

3/13 in other forms

Decimal0.230769… (the 230769 repeats forever)
Rounded0.23 (2 places), 0.231 (3 places)
Percent≈ 23.08%
Equivalent fractions6/26, 9/39, 12/52, 15/65

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 230769 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 3/13 as a decimal?

3/13 as a decimal is 0.230769… (the 230769 repeats forever). Divide 3 by 13 to get it.

What is 3/13 as a percent?

3/13 is ≈ 23.08%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 3/13 a terminating or a repeating decimal?

Repeating – the 230769 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 230769 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.