What is 47/6 as a Decimal?
47/6 = 7.8(3)
Step by step
- Simplify: 47/6 is already in simplest form
- Divide the numerator by the denominator: 47 ÷ 6 = 7.83333333
- The digits in brackets repeat forever: 7.8(3)
How the answer is worked out
A fraction is a division: 47/6 means 47 divided by 6, and doing that division gives 7.8(3). 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, 47/6 is 783.3333%. It is an improper fraction: as a mixed number it is 7 5/6.
Why calculate this?
Decimals are easier to compare and to use in calculators and spreadsheets than fractions.
- Cooking: a recipe that asks for 47/6 of a cup needs 7.833 cups, about 1,880 millilitres.
- Measuring: 47/6 of an inch is 7.8333 inches, or 198.97 millimetres.
- Money: 47/6 of a dollar is about $7.83, and 47/6 of $100 is $783.33.
A quicker way
Long division: 6 goes into 47 7 times, remainder 5.
Bring down a zero: 50 ÷ 6 = 8, remainder 2.
Bring down a zero: 20 ÷ 6 = 3, remainder 2.
The remainder 2 has come up before, so the digits from that point repeat forever: 7.8(3).
Check the answer
Work backwards: 7.833333 × 6 = 47, which is 47 once rounding is allowed for.
Rounding
Rounded to a whole number the decimal is 8, to one decimal place 7.8 and to two decimal places 7.83. 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: 9/94 as a decimal
- Simplify: 9/94 is already in simplest form
- Divide the numerator by the denominator: 9 ÷ 94 = 0.09574468
- The digits in brackets repeat forever: 0.0(9574468085106382978723404255319148936170212765)
Equivalent fractions
47/6 has the same value as 94/12, 141/18 and 470/60: multiplying the top and bottom by the same number never changes a fraction. All of them give 7.8(3) when divided out.
Comparing with nearby fractions
47/6 (7.8333) is bigger than 47/7 (6.7143) and smaller than 48/6 (8). A bigger denominator means smaller pieces, so with the same numerator the fraction gets smaller.
The reciprocal
Flipping the fraction gives 6/47 = 0.(1276595744680851063829787234042553191489361702). A number multiplied by its reciprocal is always 1: 47/6 × 6/47 = 1.
In time and money
47/6 of an hour is 470 minutes, and 47/6 of a day is 188 hours.
In a pie chart
A slice worth 47/6 of the whole takes up 2,820 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:
- 47/6 in decimal form
- 47 divided by 6
- Convert 47 over 6 to a decimal
- What is 47 ÷ 6?
- 47 out of 6 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 | 7.8(3) |
|---|---|
| Percentage | 783.3333% |
| Simplified | 47/6 |
| Type | improper fraction |
Related results
| 1/6 as a decimal | 1/6 = 0.1(6) |
| 2/6 as a decimal | 2/6 = 0.(3) |
| 3/6 as a decimal | 3/6 = 0.5 |
| 48/6 as a decimal | 48/6 = 8 |
| 46/6 as a decimal | 46/6 = 7.(6) |
The other way round: 6/47 as a decimal
Doing it in a spreadsheet
In Excel, Google Sheets or Numbers type =47/6 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
| 9/94 as a decimal | Show answer9/94 = 0.0(9574468085106382978723404255319148936170212765) |
| 33/42 as a decimal | Show answer33/42 = 0.7(857142) |
| 60/39 as a decimal | Show answer60/39 = 1.(538461) |
| 80/50 as a decimal | Show answer80/50 = 1.6 |
| 4/9 as a decimal | Show answer4/9 = 0.(4) |
| 80/82 as a decimal | Show answer80/82 = 0.(97560) |
| 79/20 as a decimal | Show answer79/20 = 3.95 |
| 55/46 as a decimal | Show answer55/46 = 1.1(9565217391304347826086) |
| 95/83 as a decimal | Show answer95/83 = 1.(14457831325301204819277108433734939759036) |
| 36/38 as a decimal | Show answer36/38 = 0.(947368421052631578) |
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 47/6 as a Decimal?
47/6 as a decimal is 7.8(3). Long-division steps and simplified fraction.
What is 47/6 as a percentage?
783.3333%. Multiply the decimal 7.833333 by 100.
What is 47/6 in simplest form?
47/6 is already in simplest form: 47 and 6 have no common factor other than 1.
Is 47/6 a terminating or a repeating decimal?
Repeating: 7.8(3). The digits in brackets go on forever.
What is 47/6 rounded to two decimal places?
7.83. Rounded to three places it is 7.833.
What is 47/6 of 100?
783.3333. Multiply 100 by 47 and divide by 6, or multiply 100 by the decimal 7.833333.
What is 47/6 as a ratio?
47:6. A ratio compares the part with the whole in the same way the fraction does.