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Fraction to Decimal Calculator
To convert a fraction to a decimal, divide the top by the bottom. 3/8 is 3 ÷ 8 = 0.375, which ends. 5/7 never ends: the long division brings back the remainder 5 after six digits, so 0.714285 repeats, written 0.(714285). A fraction ends only if its denominator has no prime factors but 2 and 5.
Divide the top by the bottom.
- 5 ÷ 7 = 0 remainder 5, so the decimal starts 0.
- Bring down a 0: 50 ÷ 7 = 7 remainder 1.
- Bring down a 0: 10 ÷ 7 = 1 remainder 3.
- Bring down a 0: 30 ÷ 7 = 4 remainder 2.
- Bring down a 0: 20 ÷ 7 = 2 remainder 6.
- Bring down a 0: 60 ÷ 7 = 8 remainder 4.
- Bring down a 0: 40 ÷ 7 = 5 remainder 5.
- The remainder 5 has come up before, so the digits from there repeat for ever: 714285.
- Rounded to 4 decimal places: 0.7143.
| Result | Value |
|---|---|
| Exact decimal | 0.(714285) |
| Written with a bar | 0. |
| Repeating block | 714285 (6 digits) |
| Rounded to 4 decimal places | 0.7143 |
| Does it end? | No: 7 has a prime factor other than 2 and 5 |
| Percent | 71.4286% |
The figure above is an example: put in your own. Type 3/8, a mixed number such as 1 3/8, or 17 out of 20. The long division is written out; repeating digits are put in brackets, and also shown with a bar. Worked out exactly in this browser and kept there; nothing is sent anywhere.
Type a fraction or a mixed number and read its exact decimal, with the long division written out and any repeating block marked in brackets and with a bar. A rounded value comes beside it.
Converting a fraction to a decimal divides the numerator by the denominator. The result either ends, like 3/8 = 0.375, or repeats a block of digits for ever, like 5/7 = 0.714285714285…
- No sign-up
- Nothing uploaded
- Shows every step
- Works offline
- Exact, no rounding errors
Key facts
| Detail | Answer |
|---|---|
| Rule | Numerator ÷ denominator, by long division |
| Example | 5/7 = 0.(714285), about 0.7143 |
| Ends when | The denominator in lowest terms is made only of 2s and 5s |
| Repeating block | At most denominator − 1 digits long; shown up to 30 |
| Refuses | A denominator of 0 |
| Where your numbers are kept | This browser only |
How to convert a fraction to a decimal by long division
Divide, bring down a zero, repeat, and watch the remainders.
Divide the top by the bottom
5 ÷ 7 = 0 remainder 5, so the decimal starts 0.
Bring down a zero
50 ÷ 7 = 7 remainder 1: the first digit after the point is 7.
Repeat with each remainder
10, 30, 20, 60, 40 give the digits 1, 4, 2, 8, 5.
Stop at a remainder of 0
The decimal ends there.
Or stop at a remainder you have seen
The digits from that point repeat: put them in brackets.
Round if you need to
0.(714285) to four places is 0.7143.
Who converts fractions to decimals
Anyone who has a fraction and needs a decimal to type, measure or compare.
Students
Long division checked step by step, repeats marked.
Woodworkers and machinists
3/16 inch as 0.1875 for a caliper.
Cooks
2/3 of a cup as 0.67 cups for a scale converter.
Spreadsheet users
Fractions turned into values a cell can hold.
Teachers
Why 1/7 repeats after six digits, shown.
Puzzle fans
The long repeats of 1/17 and 1/97.
Why 5/7 repeats: the remainders in long division
Long division explains why some fractions end and others repeat. At every step you divide a remainder by the denominator, and the remainder is always smaller than the denominator. With 7 there are only six possible non-zero remainders, 1 to 6, so within six steps one must come back, and from then on the digits repeat. If a remainder of 0 turns up first, the decimal ends.
| Division | Digit | Remainder |
|---|---|---|
| 5 ÷ 7 | 0 | 5 |
| 50 ÷ 7 | 7 | 1 |
| 10 ÷ 7 | 1 | 3 |
| 30 ÷ 7 | 4 | 2 |
| 20 ÷ 7 | 2 | 6 |
| 60 ÷ 7 | 8 | 4 |
| 40 ÷ 7 | 5 | 5: seen before, so 714285 repeats |
That is the whole of the rule the Common Core sets for Grade 7, to convert a rational number to a decimal using long division and to know that the decimal “terminates in 0s or eventually repeats” (7.NS.A.2d). It also gives the test for ending: a fraction in lowest terms ends exactly when its denominator has no prime factors other than 2 and 5, because only then is it a factor of some power of 10. The calculator states the factors in its table.
How long the repeating block can be
The repeating block can be much longer than one or two digits. Its length is never more than the denominator minus one, and for some denominators it reaches that limit: 1/7 has a block of 6 digits, 1/17 of 16 and 1/97 of 96.
| Fraction | Decimal | Digits in the repeating block |
|---|---|---|
| 1/3 | 0.(3) | 1 |
| 1/11 | 0.(09) | 2 |
| 1/27 | 0.(037) | 3 |
| 1/41 | 0.(02439) | 5 |
| 1/13 | 0.(076923) | 6 |
| 1/7 | 0.(142857) | 6 |
| 1/17 | 0.(0588235294117647) | 16 |
| 1/19 | 0.(052631578947368421) | 18 |
The sevenths share one cycle of digits, each starting at a different place: 1/7 = 0.(142857), 2/7 = 0.(285714), 3/7 = 0.(428571), 4/7 = 0.(571428), 5/7 = 0.(714285), 6/7 = 0.(857142). The calculator shows blocks up to 30 digits in full and marks longer ones with an ellipsis; the exact value is always the fraction you typed.
Brackets, bars and dots: writing a repeating decimal
Repeating decimals are written in several ways, and they all mean the same thing. The calculator uses brackets, which can be typed on any keyboard, and shows the bar version in its table.
| Style | 1/6 written this way | Where you see it |
|---|---|---|
| Brackets | 0.1(6) | Common in Europe, and typeable; used on this site |
| Bar (vinculum) | 0.1 | Usual in US and UK schools |
| Dots | 0.16̇ | A dot over the first and last repeating digit, common in UK textbooks |
| Three dots | 0.1666… | Informal; does not say which digits repeat |
The three-dot form is the one to avoid in answers: 0.1666… could be 1/6, or 0.16661666…, or anything else that starts that way. Rounded tables are worse, because they look exact. A widely copied conversion table prints 4/7 as 0.57142858; the eighth decimal place of 4/7 = 0.571428571… is 7, so rounded to eight places it is 0.57142857. Here the exact form comes first and the rounding is stated.
What this calculator does not do
This converts one fraction to its decimal. The arithmetic uses whole numbers of any size, so nothing is lost before the final rounding, and the long division is shown for the first eight digits. It does not add or multiply fractions; the fraction calculator does that and gives the decimal of the result. To go the other way, from a decimal such as 0.(714285) back to 5/7, use the decimal to fraction calculator. A denominator of 0 is refused.
This calculator or an answer-only one
What this page does that a typical answer-only widget does not.
| This page | A typical calculator | |
|---|---|---|
| Repeating digits | Marked: 0.(714285) | 0.7142857143, rounded |
| Long division | Written out | Not shown |
| Why it ends or repeats | Prime factors given | Not explained |
| Mixed numbers | 1 3/8 accepted | Often not |
| Exact arithmetic | Any size of number | Floating point, 15 or so digits |
| Your numbers leave the browser | Never | Varies |
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Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 3/8 is 3 ÷ 8 = 0.375. By hand, use long division: divide, write the digit, bring down a zero beside the remainder and divide again, until the remainder is 0 or a remainder comes back.
How do you know if a fraction will be a repeating decimal?
Reduce it to lowest terms and look at the denominator. If its only prime factors are 2 and 5, the decimal ends; any other prime factor makes it repeat. 7/40 ends (40 = 2 × 2 × 2 × 5); 7/30 repeats, because 30 has a factor of 3.
What is 5/7 as a decimal?
0.714285714285…, with the six digits 714285 repeating for ever. It is written 0.(714285) or with a bar over 714285, and rounds to 0.7143 at four places. All the sevenths use the same six digits in rotation. The long division in the calculator shows why.
What is 1/3 as a decimal?
0.(3): 0.333… with the 3 repeating. Long division of 1 by 3 leaves a remainder of 1 every time, so the digit 3 comes back for ever. 2/3 is 0.(6), which rounds to 0.67 at two places. Rounded calculator displays show 0.3333333333.
How long can the repeating part of a decimal be?
Up to one less than the denominator. 1/7 repeats every 6 digits, 1/17 every 16 and 1/97 every 96. Many denominators give shorter blocks: 1/13 repeats every 6 and 1/37 every 3. The block can never be longer than d − 1, because there are only d − 1 possible non-zero remainders when dividing by d.
How do you convert a mixed number to a decimal?
Keep the whole number and convert the fraction part, or turn it into an improper fraction first. 1 3/8 is 1 + 0.375 = 1.375, the same as 11 ÷ 8. The calculator accepts mixed numbers typed with a space. 2 3/4 is 2.75.
How do you write a repeating decimal?
Put a bar over the digits that repeat, or brackets around them: 0.1(6) for 1/6. Some books put a dot over the first and last repeating digit. Writing 0.1666… is common but does not say which digits repeat. Brackets are easiest to type.
Why does my calculator show 0.6666666667 for 2/3?
It has a fixed number of digits and rounds the last one. 2/3 never ends, so any display has to cut it off; the final 7 is rounding, not a digit of 2/3. This calculator writes 0.(6) instead and gives the rounded value separately.
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