5/13 as a Decimal

5/13 as a decimal is 0.384615…, with the 384615 repeating forever (38.46% rounded).

Result

Answer

\frac{5}{13} = \textcolor{#0b5c56}{0.\overline{384615}}

5/13 as a decimal is 0.384615384615… – the digits 384615 repeat forever.

  • Rounded to 2 places: 0.38
  • Rounded to 4 places: 0.3846
  • Percent: 38.4615%

38 of 100 squares ≈ 5/13

Step-by-step solution

The problem

\frac{5}{13}

  1. Divide 5 by 13 (long division). Write down how many times 13 goes in, carry the remainder, add a 0 and divide again. The remainder 5 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part5 ÷ 130513 × 0 = 0, 5 − 0 = 5
    Decimal place 150 ÷ 1331113 × 3 = 39, 50 − 39 = 11
    Decimal place 2110 ÷ 138613 × 8 = 104, 110 − 104 = 6
    Decimal place 360 ÷ 134813 × 4 = 52, 60 − 52 = 8
    Decimal place 480 ÷ 136213 × 6 = 78, 80 − 78 = 2
    Decimal place 520 ÷ 131713 × 1 = 13, 20 − 13 = 7
    Decimal place 670 ÷ 135513 × 5 = 65, 70 − 65 = 5

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

    = 5 \div 13 = \textcolor{#0b5c56}{0.\overline{384615}}

All the working together

\begin{aligned} &\frac{5}{13} \\[8pt] &= 5 \div 13 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{384615}}\end{aligned}

5/13 in other forms

Decimal0.384615… (the 384615 repeats forever)
Rounded0.38 (2 places), 0.385 (3 places)
Percent≈ 38.46%
Equivalent fractions10/26, 15/39, 20/52, 25/65

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 384615 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 5/13 as a decimal?

5/13 as a decimal is 0.384615… (the 384615 repeats forever). Divide 5 by 13 to get it.

What is 5/13 as a percent?

5/13 is ≈ 38.46%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 5/13 a terminating or a repeating decimal?

Repeating – the 384615 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 384615 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.