What is 21/27 as a Decimal?
21/27 = 0.(7)
Step by step
- Simplify: 21/27 = 7/9 (divide by 3)
- Divide the numerator by the denominator: 21 ÷ 27 = 0.77777778
- The digits in brackets repeat forever: 0.(7)
How the answer is worked out
A fraction is a division: 21/27 means 21 divided by 27, and doing that division gives 0.(7). 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, 21/27 is 77.7778%. 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 21/27 of a cup needs 0.778 cups, about 186.6667 millilitres.
- Measuring: 21/27 of an inch is 0.7778 inches, or 19.76 millimetres.
- Money: 21/27 of a dollar is about $0.78, and 21/27 of $100 is $77.78.
A quicker way
Long division: 27 goes into 21 0 times, remainder 21.
Bring down a zero: 210 ÷ 27 = 7, remainder 21.
The remainder 21 has come up before, so the digits from that point repeat forever: 0.(7).
Check the answer
Work backwards: 0.777778 × 27 = 21, which is 21 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 1, to one decimal place 0.8 and to two decimal places 0.78. 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: 5/55 as a decimal
- Simplify: 5/55 = 1/11 (divide by 5)
- Divide the numerator by the denominator: 5 ÷ 55 = 0.09090909
- The digits in brackets repeat forever: 0.(09)
Equivalent fractions
21/27 has the same value as 42/54, 63/81 and 210/270: multiplying the top and bottom by the same number never changes a fraction. All of them give 0.(7) when divided out.
Comparing with nearby fractions
21/27 (0.7778) is bigger than 21/28 (0.75) and smaller than 22/27 (0.8148). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 27/21 = 1.(285714). A number multiplied by its reciprocal is always 1: 21/27 × 27/21 = 1.
In time and money
21/27 of an hour is 46.67 minutes, and 21/27 of a day is 18.67 hours.
In a pie chart
A slice worth 21/27 of the whole takes up 280 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:
- 21/27 in decimal form
- 21 divided by 27
- Convert 21 over 27 to a decimal
- What is 21 ÷ 27?
- 21 out of 27 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
| Decimal | 0.(7) |
|---|---|
| Percentage | 77.7778% |
| Simplified | 7/9 |
| Type | proper fraction |
Related results
| 1/27 as a decimal | 1/27 = 0.(037) |
| 2/27 as a decimal | 2/27 = 0.(074) |
| 3/27 as a decimal | 3/27 = 0.(1) |
| 22/27 as a decimal | 22/27 = 0.(814) |
| 20/27 as a decimal | 20/27 = 0.(740) |
The other way round: 27/21 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =21/27 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
| 5/55 as a decimal | Show answer5/55 = 0.(09) |
| 17/12 as a decimal | Show answer17/12 = 1.41(6) |
| 40/69 as a decimal | Show answer40/69 = 0.(5797101449275362318840) |
| 71/46 as a decimal | Show answer71/46 = 1.5(4347826086956521739130) |
| 41/94 as a decimal | Show answer41/94 = 0.4(3617021276595744680851063829787234042553191489) |
| 14/48 as a decimal | Show answer14/48 = 0.291(6) |
| 12/29 as a decimal | Show answer12/29 = 0.(4137931034482758620689655172) |
| 89/41 as a decimal | Show answer89/41 = 2.(17073) |
| 76/77 as a decimal | Show answer76/77 = 0.(987012) |
| 8/6 as a decimal | Show answer8/6 = 1.(3) |
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 21/27 as a Decimal?
21/27 as a decimal is 0.(7). Long-division steps and simplified fraction.
What is 21/27 as a percentage?
77.7778%. Multiply the decimal 0.777778 by 100.
What is 21/27 in simplest form?
7/9. Divide the top and bottom by their greatest common factor, 3.
Is 21/27 a terminating or a repeating decimal?
Repeating: 0.(7). The digits in brackets go on forever.
What is 21/27 rounded to two decimal places?
0.78. Rounded to three places it is 0.778.
What is 21/27 of 100?
77.7778. Multiply 100 by 21 and divide by 27, or multiply 100 by the decimal 0.777778.
What is 21/27 as a ratio?
21:27, or 7:9 in simplest form. A ratio compares the part with the whole in the same way the fraction does.