What is 100/72 as a Decimal?
100/72 = 1.3(8)
Step by step
- Simplify: 100/72 = 25/18 (divide by 4)
- Divide the numerator by the denominator: 100 ÷ 72 = 1.38888889
- The digits in brackets repeat forever: 1.3(8)
How the answer is worked out
A fraction is a division: 100/72 means 100 divided by 72, and doing that division gives 1.3(8). 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, 100/72 is 138.8889%. It is an improper fraction: as a mixed number it is 1 7/18.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 100/72 of a cup needs 1.389 cups, about 333.3333 millilitres.
- Measuring: 100/72 of an inch is 1.3889 inches, or 35.28 millimetres.
- Money: 100/72 of a dollar is about $1.39, and 100/72 of $100 is $138.89.
A quicker way
Long division: 72 goes into 100 1 time, remainder 28.
Bring down a zero: 280 ÷ 72 = 3, remainder 64.
Bring down a zero: 640 ÷ 72 = 8, remainder 64.
The remainder 64 has come up before, so the digits from that point repeat forever: 1.3(8).
Check the answer
Work backwards: 1.388889 × 72 = 100, which is 100 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 1, to one decimal place 1.4 and to two decimal places 1.39. 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: 19/95 as a decimal
- Simplify: 19/95 = 1/5 (divide by 19)
- Divide the numerator by the denominator: 19 ÷ 95 = 0.2
Equivalent fractions
100/72 has the same value as 200/144, 300/216 and 1000/720: multiplying the top and bottom by the same number never changes a fraction. All of them give 1.3(8) when divided out.
Comparing with nearby fractions
100/72 (1.3889) is bigger than 100/73 (1.3699) and smaller than 101/72 (1.4028). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 72/100 = 0.72. A number multiplied by its reciprocal is always 1: 100/72 × 72/100 = 1.
In time and money
100/72 of an hour is 83.33 minutes, and 100/72 of a day is 33.33 hours.
In a pie chart
A slice worth 100/72 of the whole takes up 500 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:
- 100/72 in decimal form
- 100 divided by 72
- Convert 100 over 72 to a decimal
- What is 100 ÷ 72?
- 100 out of 72 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(8) |
|---|---|
| Percentage | 138.8889% |
| Simplified | 25/18 |
| Type | improper fraction |
Related results
| 1/72 as a decimal | 1/72 = 0.013(8) |
| 2/72 as a decimal | 2/72 = 0.02(7) |
| 3/72 as a decimal | 3/72 = 0.041(6) |
| 101/72 as a decimal | 101/72 = 1.402(7) |
| 99/72 as a decimal | 99/72 = 1.375 |
The other way round: 72/100 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =100/72 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
| 19/95 as a decimal | Show answer19/95 = 0.2 |
| 2/87 as a decimal | Show answer2/87 = 0.(0229885057471264367816091954) |
| 28/96 as a decimal | Show answer28/96 = 0.291(6) |
| 3/93 as a decimal | Show answer3/93 = 0.(032258064516129) |
| 99/30 as a decimal | Show answer99/30 = 3.3 |
| 63/85 as a decimal | Show answer63/85 = 0.7(4117647058823529) |
| 51/79 as a decimal | Show answer51/79 = 0.(6455696202531) |
| 41/91 as a decimal | Show answer41/91 = 0.(450549) |
| 19/29 as a decimal | Show answer19/29 = 0.(6551724137931034482758620689) |
| 52/70 as a decimal | Show answer52/70 = 0.7(428571) |
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 100/72 as a Decimal?
100/72 as a decimal is 1.3(8). Long-division steps and simplified fraction.
What is 100/72 as a percentage?
138.8889%. Multiply the decimal 1.388889 by 100.
What is 100/72 in simplest form?
25/18. Divide the top and bottom by their greatest common factor, 4.
Is 100/72 a terminating or a repeating decimal?
Repeating: 1.3(8). The digits in brackets go on forever.
What is 100/72 rounded to two decimal places?
1.39. Rounded to three places it is 1.389.
What is 100/72 of 100?
138.8889. Multiply 100 by 100 and divide by 72, or multiply 100 by the decimal 1.388889.
What is 100/72 as a ratio?
100:72, or 25:18 in simplest form. A ratio compares the part with the whole in the same way the fraction does.