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).
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.
The denominator is a power of 10 determined by the number of digits after the decimal point.
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.
0.375 = 375/1000. GCD(375, 1000) = 125. Divide both by 125 to get 3/8.
2.75 = 275/100 = 11/4. Since 11 ÷ 4 is 2 remainder 3, the same value is 2 3/4.
Let x = 0.(3). Then 10x = 3.(3). Subtract x: 9x = 3, so x = 3/9 = 1/3.
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.
The fraction equals the entered decimal with no error. Examples include 0.375 = 3/8 and 0.(142857) = 1/7.
A denominator cap prevents the exact fraction from being used, so the calculator returns the closest allowed rational value and reports its error.
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.
No. 0.333 is exactly 333/1000. The repeating decimal 0.(3) is exactly 1/3. Parentheses make that distinction explicit.
Nothing numerically. 11/4 is an improper fraction; 2 3/4 is the mixed-number form of the same value.
Because a maximum denominator of 100 rules out the exact fraction 314159/100000. Among denominators up to 100, 311/99 is the closest match.
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.
Yes. Negative decimals, improper fractions, and mixed numbers are supported. The sign is preserved through simplification and conversion.
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.
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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