What is 5/3 as a Decimal?
5/3 = 1.(6)
Step by step
- Simplify: 5/3 is already in simplest form
- Divide the numerator by the denominator: 5 ÷ 3 = 1.66666667
- The digits in brackets repeat forever: 1.(6)
How the answer is worked out
A fraction is a division: 5/3 means 5 divided by 3, and doing that division gives 1.(6). 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, 5/3 is 166.6667%. It is an improper fraction: as a mixed number it is 1 2/3.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 5/3 of a cup needs 1.667 cups, about 400 millilitres.
- Measuring: 5/3 of an inch is 1.6667 inches, or 42.33 millimetres.
- Money: 5/3 of a dollar is about $1.67, and 5/3 of $100 is $166.67.
A quicker way
Long division: 3 goes into 5 1 time, remainder 2.
Bring down a zero: 20 ÷ 3 = 6, remainder 2.
The remainder 2 has come up before, so the digits from that point repeat forever: 1.(6).
Check the answer
Work backwards: 1.666667 × 3 = 5, which is 5 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 2, to one decimal place 1.7 and to two decimal places 1.67. 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: 1/49 as a decimal
- Simplify: 1/49 is already in simplest form
- Divide the numerator by the denominator: 1 ÷ 49 = 0.02040816
- The digits in brackets repeat forever: 0.(020408163265306122448979591836734693877551)
Equivalent fractions
5/3 has the same value as 10/6, 15/9 and 50/30: multiplying the top and bottom by the same number never changes a fraction. All of them give 1.(6) when divided out.
Comparing with nearby fractions
5/3 (1.6667) is bigger than 5/4 (1.25) and smaller than 6/3 (2). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 3/5 = 0.6. A number multiplied by its reciprocal is always 1: 5/3 × 3/5 = 1.
In time and money
5/3 of an hour is 100 minutes, and 5/3 of a day is 40 hours.
In a pie chart
A slice worth 5/3 of the whole takes up 600 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:
- 5/3 in decimal form
- 5 divided by 3
- Convert 5 over 3 to a decimal
- What is 5 ÷ 3?
- 5 out of 3 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.(6) |
|---|---|
| Percentage | 166.6667% |
| Simplified | 5/3 |
| Type | improper fraction |
Related results
| 1/3 as a decimal | 1/3 = 0.(3) |
| 2/3 as a decimal | 2/3 = 0.(6) |
| 3/3 as a decimal | 3/3 = 1 |
| 6/3 as a decimal | 6/3 = 2 |
| 4/3 as a decimal | 4/3 = 1.(3) |
The other way round: 3/5 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =5/3 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
| 1/49 as a decimal | Show answer1/49 = 0.(020408163265306122448979591836734693877551) |
| 50/27 as a decimal | Show answer50/27 = 1.(851) |
| 84/56 as a decimal | Show answer84/56 = 1.5 |
| 39/93 as a decimal | Show answer39/93 = 0.(419354838709677) |
| 76/88 as a decimal | Show answer76/88 = 0.8(63) |
| 23/4 as a decimal | Show answer23/4 = 5.75 |
| 16/78 as a decimal | Show answer16/78 = 0.(205128) |
| 24/8 as a decimal | Show answer24/8 = 3 |
| 61/42 as a decimal | Show answer61/42 = 1.4(523809) |
| 34/83 as a decimal | Show answer34/83 = 0.(40963855421686746987951807228915662650602) |
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.
Reference this page
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Questions
What is 5/3 as a Decimal?
5/3 as a decimal is 1.(6). Long-division steps and simplified fraction.
What is 5/3 as a percentage?
166.6667%. Multiply the decimal 1.666667 by 100.
What is 5/3 in simplest form?
5/3 is already in simplest form: 5 and 3 have no common factor other than 1.
Is 5/3 a terminating or a repeating decimal?
Repeating: 1.(6). The digits in brackets go on forever.
What is 5/3 rounded to two decimal places?
1.67. Rounded to three places it is 1.667.
What is 5/3 of 100?
166.6667. Multiply 100 by 5 and divide by 3, or multiply 100 by the decimal 1.666667.
What is 5/3 as a ratio?
5:3. A ratio compares the part with the whole in the same way the fraction does.