What is 72/55 as a Decimal?
72/55 = 1.3(09)
Step by step
- Simplify: 72/55 is already in simplest form
- Divide the numerator by the denominator: 72 ÷ 55 = 1.30909091
- The digits in brackets repeat forever: 1.3(09)
How the answer is worked out
A fraction is a division: 72/55 means 72 divided by 55, and doing that division gives 1.3(09). 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, 72/55 is 130.9091%. It is an improper fraction: as a mixed number it is 1 17/55.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 72/55 of a cup needs 1.309 cups, about 314.1818 millilitres.
- Measuring: 72/55 of an inch is 1.3091 inches, or 33.25 millimetres.
- Money: 72/55 of a dollar is about $1.31, and 72/55 of $100 is $130.91.
A quicker way
Long division: 55 goes into 72 1 time, remainder 17.
Bring down a zero: 170 ÷ 55 = 3, remainder 5.
Bring down a zero: 50 ÷ 55 = 0, remainder 50.
Bring down a zero: 500 ÷ 55 = 9, remainder 5.
The remainder 5 has come up before, so the digits from that point repeat forever: 1.3(09).
Check the answer
Work backwards: 1.309091 × 55 = 72, which is 72 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 1, to one decimal place 1.3 and to two decimal places 1.31. 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: 14/98 as a decimal
- Simplify: 14/98 = 1/7 (divide by 14)
- Divide the numerator by the denominator: 14 ÷ 98 = 0.14285714
- The digits in brackets repeat forever: 0.(142857)
Equivalent fractions
72/55 has the same value as 144/110, 216/165 and 720/550: multiplying the top and bottom by the same number never changes a fraction. All of them give 1.3(09) when divided out.
Comparing with nearby fractions
72/55 (1.3091) is bigger than 72/56 (1.2857) and smaller than 73/55 (1.3273). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 55/72 = 0.763(8). A number multiplied by its reciprocal is always 1: 72/55 × 55/72 = 1.
In time and money
72/55 of an hour is 78.55 minutes, and 72/55 of a day is 31.42 hours.
In a pie chart
A slice worth 72/55 of the whole takes up 471.27 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:
- 72/55 in decimal form
- 72 divided by 55
- Convert 72 over 55 to a decimal
- What is 72 ÷ 55?
- 72 out of 55 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 | 1.3(09) |
|---|---|
| Percentage | 130.9091% |
| Simplified | 72/55 |
| Type | improper fraction |
Related results
| 1/55 as a decimal | 1/55 = 0.0(18) |
| 2/55 as a decimal | 2/55 = 0.0(36) |
| 3/55 as a decimal | 3/55 = 0.0(54) |
| 73/55 as a decimal | 73/55 = 1.3(27) |
| 71/55 as a decimal | 71/55 = 1.2(90) |
The other way round: 55/72 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =72/55 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
| 14/98 as a decimal | Show answer14/98 = 0.(142857) |
| 18/67 as a decimal | Show answer18/67 = 0.(268656716417910447761194029850746) |
| 8/10 as a decimal | Show answer8/10 = 0.8 |
| 58/72 as a decimal | Show answer58/72 = 0.80(5) |
| 36/95 as a decimal | Show answer36/95 = 0.3(789473684210526315) |
| 53/33 as a decimal | Show answer53/33 = 1.(60) |
| 7/51 as a decimal | Show answer7/51 = 0.(1372549019607843) |
| 94/84 as a decimal | Show answer94/84 = 1.1(190476) |
| 90/98 as a decimal | Show answer90/98 = 0.(918367346938775510204081632653061224489795) |
| 93/29 as a decimal | Show answer93/29 = 3.(2068965517241379310344827586) |
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 72/55 as a Decimal?
72/55 as a decimal is 1.3(09). Long-division steps and simplified fraction.
What is 72/55 as a percentage?
130.9091%. Multiply the decimal 1.309091 by 100.
What is 72/55 in simplest form?
72/55 is already in simplest form: 72 and 55 have no common factor other than 1.
Is 72/55 a terminating or a repeating decimal?
Repeating: 1.3(09). The digits in brackets go on forever.
What is 72/55 rounded to two decimal places?
1.31. Rounded to three places it is 1.309.
What is 72/55 of 100?
130.9091. Multiply 100 by 72 and divide by 55, or multiply 100 by the decimal 1.309091.
What is 72/55 as a ratio?
72:55. A ratio compares the part with the whole in the same way the fraction does.