6/13 as a Decimal

6/13 as a decimal is 0.461538…, with the 461538 repeating forever (46.15% rounded).

Result

Answer

\frac{6}{13} = \textcolor{#0b5c56}{0.\overline{461538}}

6/13 as a decimal is 0.461538461538… – the digits 461538 repeat forever.

  • Rounded to 2 places: 0.46
  • Rounded to 4 places: 0.4615
  • Percent: 46.1538%

46 of 100 squares ≈ 6/13

Step-by-step solution

The problem

\frac{6}{13}

  1. Divide 6 by 13 (long division). Write down how many times 13 goes in, carry the remainder, add a 0 and divide again. The remainder 6 came back, so the digits from decimal place 1 on repeat forever.

    StepDivideDigitRemainderWorking
    Whole part6 ÷ 130613 × 0 = 0, 6 − 0 = 6
    Decimal place 160 ÷ 134813 × 4 = 52, 60 − 52 = 8
    Decimal place 280 ÷ 136213 × 6 = 78, 80 − 78 = 2
    Decimal place 320 ÷ 131713 × 1 = 13, 20 − 13 = 7
    Decimal place 470 ÷ 135513 × 5 = 65, 70 − 65 = 5
    Decimal place 550 ÷ 1331113 × 3 = 39, 50 − 39 = 11
    Decimal place 6110 ÷ 138613 × 8 = 104, 110 − 104 = 6

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

    = 6 \div 13 = \textcolor{#0b5c56}{0.\overline{461538}}

All the working together

\begin{aligned} &\frac{6}{13} \\[8pt] &= 6 \div 13 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{0.\overline{461538}}\end{aligned}

6/13 in other forms

Decimal0.461538… (the 461538 repeats forever)
Rounded0.46 (2 places), 0.462 (3 places)
Percent≈ 46.15%
Equivalent fractions12/26, 18/39, 24/52, 30/65

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 461538 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 6/13 as a decimal?

6/13 as a decimal is 0.461538… (the 461538 repeats forever). Divide 6 by 13 to get it.

What is 6/13 as a percent?

6/13 is ≈ 46.15%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 6/13 a terminating or a repeating decimal?

Repeating – the 461538 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 461538 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.