Decimal to Fraction Calculator
Convert decimals and fractions in either direction, reduce them step by step, explore mixed numbers, repeating decimals, and denominator-limited approximations.
Repeating digits go in parentheses: 0.(3), 0.(142857), or 1.2(34).
Exact keeps the entered decimal unchanged. Approximation searches for the closest fraction under a denominator limit.
Each full bar is 1 whole. The final bar shows the fractional remainder.
The decimal and fraction share one marker because they represent exactly the same quantity.
Choose the format you need for notes, code, or typeset math.
Your conversion, step by step
Use decimal place value
The denominator is a power of 10 determined by the number of digits after the decimal point.
Find the GCD and divide both parts
375 ÷ 125 = 3
1000 ÷ 125 = 8
simplified exact fraction = 3/8
Decimals and fractions are two views of the same quantity
A terminating decimal is already a fraction written in base 10. The digits after the decimal point tell you the denominator: tenths use 10, hundredths use 100, thousandths use 1000, and so on. That is why 0.375 begins as 375/1000.
Simplifying does not change the value. It divides the numerator and denominator by the same greatest common divisor. For 375/1000, the GCD is 125, so 375 ÷ 125 = 3 and 1000 ÷ 125 = 8. Therefore 375/1000 = 3/8 exactly.
Repeating decimals are rational too. Parentheses make the repeating block explicit, so 0.(3) means 0.333… forever, while 0.333 without parentheses is the terminating decimal 333/1000. Those are close, but they are not the same number.
Decimal to Fraction Chart
The decimals you meet most often and their simplest fractions. Brackets mark digits that repeat forever.
| Decimal | Fraction | Note |
|---|---|---|
| 0.1 | 1/10 | tenth |
| 0.125 | 1/8 | eighth |
| 0.(142857) | 1/7 | repeats every 6 digits |
| 0.1(6) | 1/6 | 0.1666… |
| 0.2 | 1/5 | fifth |
| 0.25 | 1/4 | quarter |
| 0.(3) | 1/3 | 0.333… |
| 0.375 | 3/8 | |
| 0.4 | 2/5 | |
| 0.5 | 1/2 | half |
| 0.6 | 3/5 | |
| 0.625 | 5/8 | |
| 0.(6) | 2/3 | 0.666… |
| 0.75 | 3/4 | three quarters |
| 0.8 | 4/5 | |
| 0.875 | 7/8 | |
| 0.9 | 9/10 |
Sixteenths Chart for Inches and Rulers
US tape measures and drill bits are marked in sixteenths. Each row shows the reduced fraction you'd read on the ruler, its decimal, and the size in millimetres.
| Sixteenths | Reduced | Decimal inch | mm |
|---|---|---|---|
| 1/16 | 1/16 | 0.0625 | 1.59 |
| 2/16 | 1/8 | 0.125 | 3.17 |
| 3/16 | 3/16 | 0.1875 | 4.76 |
| 4/16 | 1/4 | 0.25 | 6.35 |
| 5/16 | 5/16 | 0.3125 | 7.94 |
| 6/16 | 3/8 | 0.375 | 9.52 |
| 7/16 | 7/16 | 0.4375 | 11.11 |
| 8/16 | 1/2 | 0.5 | 12.70 |
| 9/16 | 9/16 | 0.5625 | 14.29 |
| 10/16 | 5/8 | 0.625 | 15.88 |
| 11/16 | 11/16 | 0.6875 | 17.46 |
| 12/16 | 3/4 | 0.75 | 19.05 |
| 13/16 | 13/16 | 0.8125 | 20.64 |
| 14/16 | 7/8 | 0.875 | 22.22 |
| 15/16 | 15/16 | 0.9375 | 23.81 |
Worked Example: Decimal Inches to the Nearest 1/16
A drawing gives a length of 2.37 in. Your tape measure is marked in sixteenths. Where do you mark?
Step 1: Multiply the decimal part by 16 and round
Step 2: Reduce 6/16
Mark at 2 3/8 in, which is 0.005 in longer than drawn. The calculator's maximum denominator setting finds the closest fraction with any denominator up to the limit, such as 3/10. For ruler marks, use this multiply-by-16 method instead, because rulers only have halves, quarters, eighths and sixteenths.
Four conversion patterns worth knowing
Terminating decimal
0.375 = 375/1000. GCD(375, 1000) = 125. Divide both by 125 to get 3/8.
Mixed and improper
2.75 = 275/100 = 11/4. Since 11 ÷ 4 is 2 remainder 3, the same value is 2 3/4.
Repeating decimal
Let x = 0.(3). Then 10x = 3.(3). Subtract x: 9x = 3, so x = 3/9 = 1/3.
Denominator-limited approximation
3.14159 is exactly 314159/100000. With a maximum denominator of 100, the closest allowed fraction is 311/99, so the result must be labeled approximate.
Exact versus approximate
Exact
The fraction equals the entered decimal with no error. Examples include 0.375 = 3/8 and 0.(142857) = 1/7.
Approximate
A denominator cap prevents the exact fraction from being used, so the calculator returns the closest allowed rational value and reports its error.
Frequently Asked Questions
Why does 0.375 become 3/8?
0.375 is 375 thousandths, so it starts as 375/1000. The greatest common divisor is 125. Dividing both parts by 125 gives 3/8.
Is 0.333 the same as 1/3?
No. 0.333 is exactly 333/1000. The repeating decimal 0.(3) is exactly 1/3. Parentheses make that distinction explicit.
What is the difference between 11/4 and 2 3/4?
Nothing numerically. 11/4 is an improper fraction; 2 3/4 is the mixed-number form of the same value.
Why can 3.14159 become 311/99?
Because a maximum denominator of 100 rules out the exact fraction 314159/100000. Among denominators up to 100, 311/99 is the closest match.
What does the tolerance control do?
It tells you whether the best denominator-limited fraction is close enough for your chosen precision. It never changes an approximate result into an exact identity.
Can I enter negative values?
Yes. Negative decimals, improper fractions, and mixed numbers are supported. The sign is preserved through simplification and conversion.
Can I type a decimal comma, like 1,5?
Yes. 1,5 becomes 3/2 and 0,(3) becomes 1/3. Commas in groups of three are read as thousands separators instead, so 1,000 means one thousand and 1,234.5 means 1234.5.
How do I enter 0.333... with dots?
Put the repeating digits in brackets instead: 0.(3). Three dots are ambiguous, because they don't say which digits repeat. 0.1(6) and 0.(16) are different numbers.
Can I paste a Unicode fraction?
Yes. Common vulgar fractions such as ⅜, ½, and ¾ are accepted in reverse mode. A whole number can be attached too, such as 2¾.
Why does the fraction bar show only a few whole bars?
The visual is capped so large values do not flood the page. Extra whole units are summarized while the final partial bar still shows the live fractional remainder.
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