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About the decimal to fraction calculator
Type a decimal like 0.375 and get the fraction 3/8. Type 2.5 and get 5/2, or the mixed number 2 1/2. The calculator shows every step, the way it is taught in school: write the decimal over 10, 100 or 1000, then simplify.
It also works with repeating decimals. Type 0.333… or 0.1(6), or put the digits that repeat in the second box. The answer is exact: 0.1(6) is 1/6, and 0.(142857) is 1/7.
Need the other way? Switch to Fraction → decimal. Type 3/8, 2 1/2 or 1/7 and see the decimal, with the repeating part in brackets.
Features
- Exact fractions — the answer in simplest form, also for long decimals
- Mixed numbers — 2.5 is shown as 5/2 and as 2 1/2
- Repeating decimals — 0.333…, 0.1(6), 0.(142857) or a "repeating digits" box
- Every step shown — with your own numbers, ready to copy into homework
- Nearest small fraction — the closest halves, quarters, eighths … 64ths, for inches and cups
- Fraction to decimal — with the repeating block found by long division
- Negative numbers and big numbers — −1.25 is −5/4; up to 40 digits
- Decimal comma — 0,375 works too
How to turn a decimal into a fraction
- Count the decimal places. 0.375 has 3.
- Write the digits over 1 with that many zeros. 0.375 = 375/1000.
- Find the greatest common factor of the top and the bottom. For 375 and 1000 it is 125.
- Divide both by it. 375 ÷ 125 = 3 and 1000 ÷ 125 = 8, so 0.375 = 3/8.
A second example: 2.5 has 1 decimal place, so 2.5 = 25/10. The greatest common factor is 5, so 25/10 = 5/2. As a mixed number: 5 ÷ 2 = 2 remainder 1, so 5/2 = 2 1/2.
Common decimals as fractions
| Decimal | Fraction | Mixed number | Percent |
|---|---|---|---|
| 0.05 | 1/20 | – | 5% |
| 0.1 | 1/10 | – | 10% |
| 0.125 | 1/8 | – | 12.5% |
| 0.2 | 1/5 | – | 20% |
| 0.25 | 1/4 | – | 25% |
| 0.3 | 3/10 | – | 30% |
| 0.375 | 3/8 | – | 37.5% |
| 0.4 | 2/5 | – | 40% |
| 0.5 | 1/2 | – | 50% |
| 0.6 | 3/5 | – | 60% |
| 0.625 | 5/8 | – | 62.5% |
| 0.7 | 7/10 | – | 70% |
| 0.75 | 3/4 | – | 75% |
| 0.8 | 4/5 | – | 80% |
| 0.875 | 7/8 | – | 87.5% |
| 0.9 | 9/10 | – | 90% |
| 1.25 | 5/4 | 1 1/4 | 125% |
| 1.5 | 3/2 | 1 1/2 | 150% |
| 2.75 | 11/4 | 2 3/4 | 275% |
How to turn a repeating decimal into a fraction
In a repeating decimal, a block of digits goes on forever: 0.1666… (the 6 repeats) or 0.142857142857… (142857 repeats). The trick is to multiply so the repeating tails line up, then subtract.
Example: 0.1(6) = 0.1666…
- Call the number x: x = 0.1666…
- Multiply by 100 to move the point past one repeating block: 100x = 16.666…
- Multiply by 10 to move the point to the start of the block: 10x = 1.666…
- Subtract the two lines. The tails cancel: 90x = 16 − 1 = 15
- Divide: x = 15/90 = 1/6
Example: 0.(142857) = 0.142857142857…
Here the block starts right after the point. Multiply by 1,000,000: 1,000,000x = 142857.142857… Subtract x: 999,999x = 142,857. So x = 142857/999999, and the greatest common factor is 142,857. The answer is 1/7.
The calculator does the same steps with your own number. Brackets mark the block that repeats:
| Repeating decimal | Written out | Fraction |
|---|---|---|
| 0.(3) | 0.333333333333… | 1/3 |
| 0.(6) | 0.666666666666… | 2/3 |
| 0.1(6) | 0.1666666666666… | 1/6 |
| 0.8(3) | 0.8333333333333… | 5/6 |
| 0.(142857) | 0.142857142857… | 1/7 |
| 0.(1) | 0.111111111111… | 1/9 |
| 0.(09) | 0.090909090909… | 1/11 |
| 0.08(3) | 0.08333333333333… | 1/12 |
| 0.(12) | 0.121212121212… | 4/33 |
How to type a repeating decimal
- Brackets: 0.1(6) or 0.(142857). Square brackets work too: 0.1[6].
- Three dots: 0.333… or 0.1666... The calculator finds the shortest block that repeats and says how it read your number.
- The second box: type 0.1 in the first box and 6 in "Repeating digits". This is the easiest way on a phone.
If you type 0.333 without dots, the calculator takes it as exactly 333/1000. It also tells you that 1/3 is the simplest fraction that rounds to 0.333.
Fractions of an inch
Rulers and tape measures in the US use halves, quarters, eighths and sixteenths. The table below the calculator shows the nearest of these for any decimal. For 0.3 inch the nearest sixteenth is 5/16 (0.3125), off by 0.0125 inch.
| Sixteenths | Simplest | Decimal |
|---|---|---|
| 1/16 | 1/16 | 0.0625 |
| 2/16 | 1/8 | 0.125 |
| 3/16 | 3/16 | 0.1875 |
| 4/16 | 1/4 | 0.25 |
| 5/16 | 5/16 | 0.3125 |
| 6/16 | 3/8 | 0.375 |
| 7/16 | 7/16 | 0.4375 |
| 8/16 | 1/2 | 0.5 |
| 9/16 | 9/16 | 0.5625 |
| 10/16 | 5/8 | 0.625 |
| 11/16 | 11/16 | 0.6875 |
| 12/16 | 3/4 | 0.75 |
| 13/16 | 13/16 | 0.8125 |
| 14/16 | 7/8 | 0.875 |
| 15/16 | 15/16 | 0.9375 |
Fraction to decimal: ends or repeats?
Divide the top by the bottom. Simplify the fraction first, then look at the bottom number:
- If its only prime factors are 2 and 5, the decimal ends: 3/8 = 0.375, 7/20 = 0.35.
- If it has any other prime factor (3, 7, 11 …), the decimal repeats forever: 1/3 = 0.(3), 1/7 = 0.(142857).
The calculator shows which prime factor makes a decimal repeat, and after how many digits the block comes back.
Frequently asked questions
How do I write 0.375 as a fraction?
0.375 = 375/1000. The greatest common factor of 375 and 1000 is 125, so 0.375 = 3/8.
How do I convert a repeating decimal to a fraction?
Multiply the number so that the repeating part lines up, then subtract. For 0.333…: 10x = 3.333… and x = 0.333…, so 9x = 3 and x = 3/9 = 1/3. The calculator shows these steps for any repeating decimal.
Is 0.999… really equal to 1?
Yes. With the same steps: 10x = 9.999… and x = 0.999…, so 9x = 9 and x = 1. There is no number between 0.999… and 1, so they are the same number.
Why does 0.333 not give 1/3?
0.333 stops after three 3s, so it is exactly 333/1000. Only 0.333… (with the 3s going on forever) is 1/3. The calculator shows 1/3 as "the simplest fraction that rounds to 0.333".
What is a mixed number?
A whole number and a fraction together, like 2 1/2. It is the same as the improper fraction 5/2. The calculator shows both.
Can I convert negative decimals?
Yes. −1.25 becomes −5/4, or −1 1/4 as a mixed number. The steps are done without the minus sign, and it is put back at the end.
How do I type the decimal on a phone?
Type the number in the first box. For a repeating decimal, type the digits that repeat in the second box, so you do not need brackets or dots.
Related tools
- Fraction Calculator — add, subtract, multiply and divide fractions with steps
- Percentage Calculator — X% of Y, X is what percent of Y, percent change
- GCF and LCM Calculator — the greatest common factor used to simplify fractions
- Ratio Calculator — simplify a ratio like 16 : 9
- MM to Inches — millimetres to inches, with fractions of an inch
How to use it
- Choose Decimal → fraction (or Fraction → decimal)
- Type the decimal, for example 0.375 or 2.5
- For a repeating decimal, type 0.1(6) or 0.333…, or put the repeating digits in the second box
- Read the fraction and the mixed number in the result
- Read the steps and the nearest small fraction under the form, or press Copy
