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What is 20/87 as a Decimal?

20/87 = 0.(2298850574712643678160919540)

Step by step

  1. Simplify: 20/87 is already in simplest form
  2. Divide the numerator by the denominator: 20 ÷ 87 = 0.22988506
  3. The digits in brackets repeat forever: 0.(2298850574712643678160919540)

How the answer is worked out

A fraction is a division: 20/87 means 20 divided by 87, and doing that division gives 0.(2298850574712643678160919540). 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, 20/87 is 22.9885%. It is a proper fraction, so its value is between 0 and 1, and it is less 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 20/87 of a cup needs 0.23 cups, about 55.1724 millilitres.
  • Measuring: 20/87 of an inch is 0.2299 inches, or 5.84 millimetres.
  • Money: 20/87 of a dollar is about $0.23, and 20/87 of $100 is $22.99.

A quicker way

Long division: 87 goes into 20 0 times, remainder 20.

Bring down a zero: 200 ÷ 87 = 2, remainder 26.

Bring down a zero: 260 ÷ 87 = 2, remainder 86.

Bring down a zero: 860 ÷ 87 = 9, remainder 77.

Bring down a zero: 770 ÷ 87 = 8, remainder 74.

Bring down a zero: 740 ÷ 87 = 8, remainder 44.

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

Check the answer

Work backwards: 0.229885 × 87 = 20, which is 20 once rounding is allowed for.

Rounding

Rounded to a whole number the decimal is 0, to one decimal place 0.2 and to two decimal places 0.23. 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: 5/11 as a decimal

  1. Simplify: 5/11 is already in simplest form
  2. Divide the numerator by the denominator: 5 ÷ 11 = 0.45454545
  3. The digits in brackets repeat forever: 0.(45)

Equivalent fractions

20/87 has the same value as 40/174, 60/261 and 200/870: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.(2298850574712643678160919540) when divided out.

Comparing with nearby fractions

20/87 (0.2299) is bigger than 20/88 (0.2273) and smaller than 21/87 (0.2414). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.

The reciprocal

Flipping the fraction gives 87/20 = 4.35. A number multiplied by its reciprocal is always 1: 20/87 × 87/20 = 1.

In time and money

20/87 of an hour is 13.79 minutes, and 20/87 of a day is 5.52 hours.

In a pie chart

A slice worth 20/87 of the whole takes up 82.76 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:

  • 20/87 in decimal form
  • 20 divided by 87
  • Convert 20 over 87 to a decimal
  • What is 20 ÷ 87?
  • 20 out of 87 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.(2298850574712643678160919540)
Percentage22.9885%
Simplified20/87
Typeproper fraction

Related results

1/87 as a decimal

1/87 = 0.(0114942528735632183908045977)

2/87 as a decimal

2/87 = 0.(0229885057471264367816091954)

3/87 as a decimal

3/87 = 0.(0344827586206896551724137931)

21/87 as a decimal

21/87 = 0.(2413793103448275862068965517)

19/87 as a decimal

19/87 = 0.(2183908045977011494252873563)

The other way round: 87/20 as a decimal

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =20/87 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

5/11 as a decimal
Show answer

5/11 = 0.(45)

27/78 as a decimal
Show answer

27/78 = 0.3(461538)

56/74 as a decimal
Show answer

56/74 = 0.(756)

8/90 as a decimal
Show answer

8/90 = 0.0(8)

80/52 as a decimal
Show answer

80/52 = 1.(538461)

59/13 as a decimal
Show answer

59/13 = 4.(538461)

19/71 as a decimal
Show answer

19/71 = 0.(26760563380281690140845070422535211)

46/85 as a decimal
Show answer

46/85 = 0.5(4117647058823529)

82/61 as a decimal
Show answer

82/61 = 1.(344262295081967213114754098360655737704918032786885245901639)

88/61 as a decimal
Show answer

88/61 = 1.(442622950819672131147540983606557377049180327868852459016393)

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 20/87 as a Decimal?

20/87 as a decimal is 0.(2298850574712643678160919540). Long-division steps and simplified fraction.

What is 20/87 as a percentage?

22.9885%. Multiply the decimal 0.229885 by 100.

What is 20/87 in simplest form?

20/87 is already in simplest form: 20 and 87 have no common factor other than 1.

Is 20/87 a terminating or a repeating decimal?

Repeating: 0.(2298850574712643678160919540). The digits in brackets go on forever.

What is 20/87 rounded to two decimal places?

0.23. Rounded to three places it is 0.230.

What is 20/87 of 100?

22.9885. Multiply 100 by 20 and divide by 87, or multiply 100 by the decimal 0.229885.

What is 20/87 as a ratio?

20:87. A ratio compares the part with the whole in the same way the fraction does.