Decimal to Fraction Calculator & Converter
Type any decimal, and this decimal to fraction calculator turns it into a fraction in simplest form, with the whole number, numerator, and denominator shown separately. It works with terminating decimals like 0.75, negative decimals like −2.125, and repeating decimals typed in brackets, such as 0.(3) or 0.1(6).
Answer
Step-by-step solution
Tip: for a repeating decimal, type the digits before the repeat in the first box (0.1) and the repeating digits in the second box (6), or use brackets: 0.1(6). Press Enter to calculate.
Decimal to Fraction Calculator at a Glance
Decimal to fraction calculator converts a decimal number to a simplified fraction by writing the digits after the point over 10, 100, or 1000, using one zero for each decimal place. Then divide the top and bottom by their greatest common factor: 0.36 → 36/100 → ÷ 4 → 9/25. Repeating decimals use a different method.
0.36 → 36/100 → ÷ 4 → 9/25
How to Use a Decimal to Fraction Calculator
The decimal to fraction calculator needs one input and gives three answer fields.
01 Type your decimal
Use a minus sign for negatives and brackets for repeating digits.
02 Press Calculate or Enter
03 Read the result
Then open the step-by-step solution below it.
To check any answer, divide the numerator by the denominator. You should get your decimal back. You can solve Fractions through our Fraction Calculator.
Your Input
The box takes a normal decimal (0.36), a negative decimal (−2.125), or a repeating decimal. For a repeating decimal, put non-repeating digits in the first box, then enter the repeating number in the second box.
Textbooks show repeating digits with a bar on top. You can’t type a bar, so use a second box.
In your book | Means |
|---|---|
0.3 with a bar over the 3 | 0.333… |
0.16 with a bar over both digits | 0.161616… |
Result
The answer appears as a mixed number, in simplest form, and as a percent. For 2.625, the fields read 2, 5, and 8, which means 2 ⅝. As an improper fraction, that is 21/8, and as a percent, 262.5%.
Field 1
Whole Number
This is the part of the decimal before the point. For 6.125, it is 6. For a negative decimal, it carries the sign: −2.125 gives a whole number of −2 and a fraction part of 1/8. That reads as −2 1/8.
Field 2
Numerator
The numerator is the top number of the simplified fraction. Numerator digits often look different from your decimal because the decimal to fraction calculator has already reduced the fraction: 0.625 → 625/1000 → ÷ 125 → 5/8.
Field 3
Denominator
The denominator is the number below in the simplified fraction. Use the denominator as a quick check. If you typed a decimal that stops, the simplified denominator can only have 2 and 5 as prime factors. If you see a factor of 3, 7, or 11, your input is a repeating decimal.
Step-by-Step Solution
The steps follow the same method you use on paper so that you can copy them into your work. For 0.36, the calculator shows:
- Place value: two decimal places.
- Raw fraction: 36/100.
- Greatest common factor: 4.
- Simplest form: 36 ÷ 4 over 100 ÷ 4 = 9/25.
Why does the result depend on decimal places?
The decimal to fraction calculator converts exactly the digits you type, no more and no less. Each extra digit changes the denominator:
You type | What it means | Fraction |
|---|---|---|
0.333 | Stops after 3 places | 333/1000 |
0.33333 | Stops after 5 places | 33333/100000 |
0.3… | 3 repeats forever | 1/3 |
Rounding works the same way. 3/8 is 0.375. Round it to 0.38 and convert back, and you get 19/50, a different number. Enter every digit you have, or use the repeating number box for repeating digits.
Understanding Decimal to Fraction Conversion
Conversion always works for decimals that stop or repeat, because place value already gives a terminating decimal its denominator.
Every decimal is already a fraction
This is for every decimal that stops. Repeating decimals are fractions too, but over 9s instead of a power of 10. Decimals that never stop and never repeat, like π, are not fractions at all. As 0.36 is thirty-six hundredths, it is 36/100.
Why is it helpful to convert a decimal to a fraction?
- Exact answers. 1/3 is exact. 0.33 is only close, and every rounded digit drifts further from the true value.
- Homework and tests. The Grade 8 Common Core standard (8.NS.A.1) asks students to turn repeating decimals into fractions. When a question asks for the simplest form, a decimal answer is usually marked wrong.
- Measurements. Rulers, tape measures, and drill bits are marked in fractions such as sixteenths, so 0.625 inches is read as 5/8 inch.
Want to solve these without the calculator?
Three methods cover every decimal you have:
- Decimals that stop: digits over a power of 10, then simplify. See the steps below.
- Bigger than one or negative: set the whole number or the minus sign aside first.
- Repeating decimals: shift and subtract.
Work each one on paper, then check your answer with the decimal to fraction calculator.
Steps to Convert a Decimal to a Fraction
- Count the decimal places to pick 10, 100, or 1000.
- Find the greatest common factor of the top and bottom.
- Divide both by it.
Follow 0.36 through all steps below. This method only works for decimals that stop. Putting a repeating decimal over 1000 gives a wrong answer, so use the repeating method instead.
Count the decimal places
Count only the digits after the point. This number tells you how many 0s come after 1. Don’t add zeros for digits before the point. As in 0.36, there are 2 places after the decimal, so we use two zeros.
Find the greatest common factor
The GCF of 36 and 100 is 4. For any decimal that stops, the denominator is built only from 2s and 5s (10 = 2 × 5), so the GCF is too. That means you only need to test 2 and 5.
Divide both by it
36 ÷ 4 = 9 and 100 ÷ 4 = 25, so 0.36 = 9/25. The value stays the same because dividing the top and bottom by 4 is the same as dividing by 4/4, which equals 1.
Decimal to Fraction Formula
For a decimal that stops:
decimal = N ÷ 10ⁿ
N is the decimal written without the point, and n is the number of decimal places. 0.36 → 36 ÷ 10² → 36/100 → 9/25.
For a repeating decimal, use only the part after the point:
fraction = (A − B) ÷ (r nines followed by n zeros)
- A: the digits up to the end of the first repeating block
- B: the digits before the repeat starts
- r: how many digits repeat
- n: how many digits come before the repeat
0.1(6): A = 16, B = 1, one 9 and one 0 → (16 − 1) ÷ 90 = 15/90 = 1/6.
The formula and steps give the same answer. The steps show why it works, and the formula is quicker once you’ve practised.
Decimals greater than one
This is the way to convert a decimal above 1, and both give the same answer:
Method | 6.125 |
|---|---|
Split | 6 + 0.125 → 6 + 1/8 → 6 1/8 |
All digits | 6125/1000 → ÷ 125 → 49/8 |
Splitting keeps the numbers small. The all-digits method gives an improper fraction straight away, which is simple for further calculation. The decimal to fraction calculator puts the whole number in its own field.
How to Convert a Negative Decimal to a Fraction
Set the minus sign aside, convert the positive number, then put the sign back on the answer. You can also type the minus sign straight into the decimal to fraction calculator.
Type | Decimal | Fraction |
|---|---|---|
Less than 1 | −0.36 | −9/25 |
Bigger than 1 | −2.125 | −17/8 = −2 1/8 |
Repeating | −0.(6) | −2/3 |
Write −9/25. A minus on both parts, −9/−25, makes the fraction positive.
How to Convert a Repeating Decimal to a Fraction
A repeating decimal has digits that go on forever in a pattern. In a pure repeating decimal like 0.3…, the repeat starts right after the point. In a mixed one like 0.166…, a few digits come first.
The examples below cover a pure repeat 0.(3) and a mixed repeat 0.1(6).
For a repeating decimal, shift and subtract instead
Let x be the decimal. Make a second copy, shifted so its endless tail lines up exactly with the first. Subtract the two copies: the tails cancel, and an ordinary whole number is left.
- Pure repeat: multiply by 10 for each repeating digit (1 digit → 10x, 2 digits → 100x, 3 digits → 1000x), then subtract x.
- Mixed repeat: make two copies. Shift one to where the repeat starts (10ⁿx) and the other one full block further (10ⁿ⁺ʳx). Subtract the smaller from the larger.
Before you subtract, check that the digits after the point match in both lines. With the wrong multiplier, they won’t. For 0.(27), using 10x gives 2.7272… − 0.2727… = 2.4545…, which still repeats. Use 100x instead: 100x − x = 27, so 99x = 27 and x = 3/11.
A repeating decimal: 0.3…
If the 3s go on forever, write 0.333…. Stopped after three places, 0.333 is a different number: 333/1000.
x = 0.333…
10x = 3.333…
10x − x = 3, so 9x = 3
x = 3/9 = 1/3
A single repeating digit always ends up over 9:
Repeating decimal | Fraction |
|---|---|
0.(1) | 1/9 |
0.(3) | 3/9 = 1/3 |
0.(6) | 6/9 = 2/3 |
0.(9) | 9/9 = 1 |
Check: 3 × 0.3… = 0.9…, which equals exactly 1. Type 0.(3) into the decimal to fraction calculator, and the steps show this same subtraction.
A mixed repeating decimal: 0.166…
Here the 1 appears once and only the 6 repeats.
x = 0.1666…
10x = 1.666…
100x = 16.666…
100x − 10x = 15, so 90x = 15
x = 15/90 = 1/6
10x shifts to where the repeat starts, and 100x moves one full block further. The formula gives the same result: (16 − 1) ÷ 90 = 15/90 = 1/6.
Decimal to Fraction Chart
The values are grouped by family, so you can spot the patterns. Every eighth is a multiple of 0.125, and every sixteenth is a multiple of 0.0625. All values are exact. Repeating decimals are written in brackets, never rounded.
Family | Decimal = fraction |
|---|---|
Halves and quarters | 0.5 = 1/2 · 0.25 = 1/4 · 0.75 = 3/4 |
Eighths | 0.125 = 1/8 · 0.375 = 3/8 · 0.625 = 5/8 · 0.875 = 7/8 |
Sixteenths | 0.0625 = 1/16 · 0.1875 = 3/16 · 0.3125 = 5/16 · 0.4375 = 7/16 |
Sixteenths (cont.) | 0.5625 = 9/16 · 0.6875 = 11/16 · 0.8125 = 13/16 · 0.9375 = 15/16 |
Thirty-seconds and sixty-fourths | 0.03125 = 1/32 · 0.015625 = 1/64 |
Fifths and tenths | 0.1 = 1/10 · 0.2 = 1/5 · 0.4 = 2/5 · 0.6 = 3/5 · 0.8 = 4/5 |
Repeating | 0.(3) = 1/3 · 0.(6) = 2/3 · 0.1(6) = 1/6 · 0.8(3) = 5/6 · 0.(1) = 1/9 · 0.08(3) = 1/12 · 0.(142857) = 1/7 |
Tape measures are usually marked in sixteenths of an inch. If your measurement falls between marks, multiply it by 16, round to the nearest whole number, and put that over 16: 0.42 × 16 = 6.72 → 7/16 inch. For any value not listed, the decimal to fraction calculator gives the exact fraction.
Advantages and disadvantages of using a chart versus the formula for decimals to fraction
Chart | Formula or calculator | |
|---|---|---|
Speed | Instant, if value is listed | A few seconds |
Coverage | Only the listed values | Every decimal that stops or repeats |
Exactness | Exact here, but some charts are rounded | Exact |
Best for | Measuring, common test values | Unusual decimals, showing working |
You don’t need to memorise the whole chart. Learn 1/2, 1/4, 1/8, 1/3 and 1/5, and you can build most of the others: 0.875 is 7 × 0.125, so it is 7/8. Use the chart for a quick estimate and the formula when you need to show working.
Common Mistakes
These slips cause most wrong answers when converting by hand. A few also explain results from the decimal to fraction calculator that look surprising at first.
Mistake | Wrong | Right | Quick check |
|---|---|---|---|
Skipping a zero after the point | 0.03 → 3/10 | 3/100 | Say it: “three hundredths” |
Counting the whole number as places | 2.5 → 25/100 | 25/10 = 5/2 | Count only digits after the point |
Dropping the whole number | 2.5 → 1/2 | 2 1/2 | The answer must be more than 1 |
Stopping before simplest form | 0.36 → 36/100 | 9/25 | Do the top and bottom still share 2 or 5? |
Treating a stopped decimal as repeating | 0.333 → 1/3 | 333/1000 | Is there a bar, dots, or brackets? |
Putting a repeating decimal over 10ⁿ | 0.(3) → 3/10 | 1/3 | Repeats go over 9s |
Wrong multiplier | 0.(27): 10x − x | 100x − x → 3/11 | Do the tails line up? |
Brackets in the wrong place | 0.1666… as 0.(16) | 0.1(6) = 1/6 | Bracket only the repeating digits |
Minus on both parts | −0.625 → −5/−8 | −5/8 | One sign, in front |
Splitting a negative mixed number | −2.125 → −2 + 1/8 | −2 1/8 = −17/8 | The sign covers the whole number |
Converting Fractions to Decimals
To go the other way, divide the numerator by the denominator: 21 ÷ 8 = 2.625. That same division is the quickest way to check any answer. For division and why some fractions never stop repeating, use the Fraction to Decimal calculator.