13/7 as a Decimal

13/7 as a decimal is 1.857142…, the same as 1 6/7 or about 185.71%.

Result

Answer

\frac{13}{7} = \textcolor{#0b5c56}{1.\overline{857142}}

13/7 as a decimal is 1.857142857142… – the digits 857142 repeat forever.

  • Rounded to 2 places: 1.86
  • Rounded to 4 places: 1.8571
  • Percent: 185.7143%

1 whole + 6 of 7 equal parts

Step-by-step solution

The problem

\frac{13}{7}

  1. Divide 13 by 7 (long division). Write down how many times 7 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 part13 ÷ 7167 × 1 = 7, 13 − 7 = 6
    Decimal place 160 ÷ 7847 × 8 = 56, 60 − 56 = 4
    Decimal place 240 ÷ 7557 × 5 = 35, 40 − 35 = 5
    Decimal place 350 ÷ 7717 × 7 = 49, 50 − 49 = 1
    Decimal place 410 ÷ 7137 × 1 = 7, 10 − 7 = 3
    Decimal place 530 ÷ 7427 × 4 = 28, 30 − 28 = 2
    Decimal place 620 ÷ 7267 × 2 = 14, 20 − 14 = 6

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

    = 13 \div 7 = \textcolor{#0b5c56}{1.\overline{857142}}

All the working together

\begin{aligned} &\frac{13}{7} \\[8pt] &= 13 \div 7 && \textcolor{#5b6660}{\textsf{divide}} \\[8pt] &= \textcolor{#0b5c56}{1.\overline{857142}}\end{aligned}

13/7 in other forms

Decimal1.857142… (the 857142 repeats forever)
Rounded1.86 (2 places), 1.857 (3 places)
Percent≈ 185.71%
Mixed number1 6/7
Equivalent fractions26/14, 39/21, 52/28, 65/35

Why it repeats

In lowest terms the denominator is 7 = 7. It has the prime factor 7, which does not divide any power of 10, so the long division never ends: the 857142 repeats forever.

Fractions over 7 as decimals

FractionDecimalPercent
1/70.142857…≈ 14.29%
2/70.285714…≈ 28.57%
3/70.428571…≈ 42.86%
4/70.571428…≈ 57.14%
5/70.714285…≈ 71.43%
6/70.857142…≈ 85.71%
8/71.142857…≈ 114.29%
9/71.285714…≈ 128.57%
10/71.428571…≈ 142.86%
11/71.571428…≈ 157.14%
12/71.714285…≈ 171.43%
13/71.857142…≈ 185.71%
15/72.142857…≈ 214.29%
16/72.285714…≈ 228.57%
17/72.428571…≈ 242.86%
18/72.571428…≈ 257.14%
19/72.714285…≈ 271.43%
20/72.857142…≈ 285.71%

Frequently asked questions

What is 13/7 as a decimal?

13/7 as a decimal is 1.857142… (the 857142 repeats forever). Divide 13 by 7 to get it.

What is 13/7 as a percent?

13/7 is ≈ 185.71%: multiply the decimal by 100 (move the decimal point two places to the right).

Is 13/7 a terminating or a repeating decimal?

Repeating – the 857142 repeats forever. In lowest terms the denominator is 7 = 7. It has the prime factor 7, which does not divide any power of 10, so the long division never ends: the 857142 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.