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What is 47/71 as a Decimal?

47/71 = 0.(66197183098591549295774647887323943)

Step by step

  1. Simplify: 47/71 is already in simplest form
  2. Divide the numerator by the denominator: 47 ÷ 71 = 0.66197183
  3. The digits in brackets repeat forever: 0.(66197183098591549295774647887323943)

How the answer is worked out

A fraction is a division: 47/71 means 47 divided by 71, and doing that division gives 0.(66197183098591549295774647887323943). The division never ends, because the simplified denominator has a prime factor other than 2 or 5. The digits in brackets repeat forever.

As a percentage, 47/71 is 66.1972%. It is a proper fraction, so its value is between 0 and 1, and it is more than one half.

Why calculate this?

Decimals are easier to compare and to use in calculators and spreadsheets than fractions.

  • Cooking: a recipe that asks for 47/71 of a cup needs 0.662 cups, about 158.8732 millilitres.
  • Measuring: 47/71 of an inch is 0.662 inches, or 16.81 millimetres.
  • Money: 47/71 of a dollar is about $0.66, and 47/71 of $100 is $66.2.

A quicker way

Long division: 71 goes into 47 0 times, remainder 47.

Bring down a zero: 470 ÷ 71 = 6, remainder 44.

Bring down a zero: 440 ÷ 71 = 6, remainder 14.

Bring down a zero: 140 ÷ 71 = 1, remainder 69.

Bring down a zero: 690 ÷ 71 = 9, remainder 51.

Bring down a zero: 510 ÷ 71 = 7, remainder 13.

Keep going until a remainder repeats; from then on the digits repeat as well.

Check the answer

Work backwards: 0.661972 × 71 = 47, which is 47 once rounding is allowed for.

Rounding

Rounded to a whole number the decimal is 1, to one decimal place 0.7 and to two decimal places 0.66. Round only at the end: rounding halfway through a calculation can change the last digit.

The formula explained

decimal = numerator ÷ denominator. The numerator is the top number and counts the pieces; the denominator is the bottom number and says how many equal pieces make a whole. Dividing the top by the bottom gives the size of the fraction as a decimal.

Another worked example: 10/81 as a decimal

  1. Simplify: 10/81 is already in simplest form
  2. Divide the numerator by the denominator: 10 ÷ 81 = 0.12345679
  3. The digits in brackets repeat forever: 0.(123456790)

Equivalent fractions

47/71 has the same value as 94/142, 141/213 and 470/710: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.(66197183098591549295774647887323943) when divided out.

Comparing with nearby fractions

47/71 (0.662) is bigger than 47/72 (0.6528) and smaller than 48/71 (0.6761). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.

The reciprocal

Flipping the fraction gives 71/47 = 1.(5106382978723404255319148936170212765957446808). A number multiplied by its reciprocal is always 1: 47/71 × 71/47 = 1.

In time and money

47/71 of an hour is 39.72 minutes, and 47/71 of a day is 15.89 hours.

In a pie chart

A slice worth 47/71 of the whole takes up 238.31 degrees of the circle, because a full turn is 360 degrees. That is the angle to draw when you make the chart by hand with a protractor.

Other ways to ask this

The same calculation is often asked in other words. All of these have the answer above:

  • 47/71 in decimal form
  • 47 divided by 71
  • Convert 47 over 71 to a decimal
  • What is 47 ÷ 71?
  • 47 out of 71 as a decimal number

Terms used on this page

  • Numerator: the top number of a fraction.
  • Denominator: the bottom number, the number of equal parts in a whole.
  • Terminating decimal: a decimal that ends, such as 0.25.
  • Repeating decimal: a decimal whose digits repeat forever, such as 0.333….

The answer in other forms

Decimal0.(66197183098591549295774647887323943)
Percentage66.1972%
Simplified47/71
Typeproper fraction

Related results

1/71 as a decimal

1/71 = 0.(01408450704225352112676056338028169)

2/71 as a decimal

2/71 = 0.(02816901408450704225352112676056338)

3/71 as a decimal

3/71 = 0.(04225352112676056338028169014084507)

48/71 as a decimal

48/71 = 0.(67605633802816901408450704225352112)

46/71 as a decimal

46/71 = 0.(64788732394366197183098591549295774)

The other way round: 71/47 as a decimal

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =47/71 into any cell. Replace the numbers with cell references (for example A1 and B1) to reuse the formula for a whole column.

Common mistakes

Dividing the denominator by the numerator flips the fraction. A bar over (or brackets around) digits means they repeat forever.

Practice examples

10/81 as a decimal
Show answer

10/81 = 0.(123456790)

16/44 as a decimal
Show answer

16/44 = 0.(36)

57/24 as a decimal
Show answer

57/24 = 2.375

71/46 as a decimal
Show answer

71/46 = 1.5(4347826086956521739130)

8/36 as a decimal
Show answer

8/36 = 0.(2)

78/50 as a decimal
Show answer

78/50 = 1.56

31/56 as a decimal
Show answer

31/56 = 0.553(571428)

41/55 as a decimal
Show answer

41/55 = 0.7(45)

76/56 as a decimal
Show answer

76/56 = 1.3(571428)

38/42 as a decimal
Show answer

38/42 = 0.(904761)

Calculate another

How this answer was calculated

The result is worked out from the numbers in this page's address when the page is opened, using exact arithmetic wherever possible and rounding only for display. Nothing is copied from a printed table. If you think an answer is wrong, please tell us through the contact page and we will check it.

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Questions

What is 47/71 as a Decimal?

47/71 as a decimal is 0.(66197183098591549295774647887323943). Long-division steps and simplified fraction.

What is 47/71 as a percentage?

66.1972%. Multiply the decimal 0.661972 by 100.

What is 47/71 in simplest form?

47/71 is already in simplest form: 47 and 71 have no common factor other than 1.

Is 47/71 a terminating or a repeating decimal?

Repeating: 0.(66197183098591549295774647887323943). The digits in brackets go on forever.

What is 47/71 rounded to two decimal places?

0.66. Rounded to three places it is 0.662.

What is 47/71 of 100?

66.1972. Multiply 100 by 47 and divide by 71, or multiply 100 by the decimal 0.661972.

What is 47/71 as a ratio?

47:71. A ratio compares the part with the whole in the same way the fraction does.