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.

Last updated: August 2026 | By Workshelve Team

Repeating digits go in parentheses: 0.(3), 0.(142857), or 1.2(34).

Conversion strategy

Exact keeps the entered decimal unchanged. Approximation searches for the closest fraction under a denominator limit.

Exact mode reduces the decimal to its mathematically identical fraction with no denominator cap.
Fraction display
Fraction result
3/8
Exact
Improper
3/8
Mixed
3/8
Live fraction bar
3/8

Each full bar is 1 whole. The final bar shows the fractional remainder.

Number line
0
0.5
1
0.375 = 3/8

The decimal and fraction share one marker because they represent exactly the same quantity.

Copy output

Choose the format you need for notes, code, or typeset math.

Your conversion, step by step

Step 1

Use decimal place value

0.375 = 375 / 1000

The denominator is a power of 10 determined by the number of digits after the decimal point.

Step 2

Find the GCD and divide both parts

GCD(|375|, 1000) = 125
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.

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 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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