What is 20/67 as a Decimal?

Step by step

1. Simplify: 20/67 is already in simplest form
2. Divide the numerator by the denominator: 20 ÷ 67 = 0.29850746
3. The digits in brackets repeat forever: 0.(298507462686567164179104477611940)

How the answer is worked out

A fraction is a division: 20/67 means 20 divided by 67, and doing that division gives 0.(298507462686567164179104477611940). 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, 20/67 is 29.8507%. 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 20/67 of a cup needs 0.299 cups, about 71.6418 millilitres.
• Measuring: 20/67 of an inch is 0.2985 inches, or 7.58 millimetres.
• Money: 20/67 of a dollar is about $0.3, and 20/67 of $100 is $29.85.

A quicker way

Long division: 67 goes into 20 0 times, remainder 20.

Bring down a zero: 200 ÷ 67 = 2, remainder 66.

Bring down a zero: 660 ÷ 67 = 9, remainder 57.

Bring down a zero: 570 ÷ 67 = 8, remainder 34.

Bring down a zero: 340 ÷ 67 = 5, remainder 5.

Bring down a zero: 50 ÷ 67 = 0, remainder 50.

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

Check the answer

Work backwards: 0.298507 × 67 = 20, which is 20 once rounding is allowed for.

Rounding

Rounded to a whole number the decimal is 0, to one decimal place 0.3 and to two decimal places 0.30. 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: 5/66 as a decimal

1. Simplify: 5/66 is already in simplest form
2. Divide the numerator by the denominator: 5 ÷ 66 = 0.07575758
3. The digits in brackets repeat forever: 0.0(75)

Other ways to ask this

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

• 20/67 in decimal form
• 20 divided by 67
• Convert 20 over 67 to a decimal
• What is 20 ÷ 67?
• 20 out of 67 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

Related results

The other way round: 67/20 as a decimal

Doing it in a spreadsheet

In Excel, Google Sheets or Numbers type =20/67 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

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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