FracConv

Decimal to Fraction Converter

Continued-fraction approximation for accuracy.

Decimal

Fraction

3 / 4

What you entered

Decimal: 0.75

1
Continued-fraction step 1
⌊0.75⌋ = 0= 0/1
2
Continued-fraction step 2
⌊1.3333⌋ = 1= 1/1
3
Continued-fraction step 3
⌊3⌋ = 3= 3/4

Result

Fraction: 3 / 4

0.75 written as a fraction is 3 / 4.

Decimals converted to fractions in lowest terms

Each decimal is written as a fraction and reduced by the greatest common divisor.

Decimal	Fraction
0.125	1/8
0.25	1/4
0.333	333/1000
0.5	1/2
0.6	3/5
0.75	3/4
1.5	3/2
2.25	9/4

The 0.333 row is the important caution: it converts to 333/1000, not 1/3, because 0.333 is a terminating decimal that merely resembles a third. A true one third is 0.3 recurring and cannot be written exactly as a terminating decimal at all, so no finite input will produce 1/3. Decimals that terminate always convert to a fraction whose denominator is a power of 10 reduced down - which is why halves, quarters, fifths and eighths convert cleanly while thirds and sevenths never do.

Finding the simplest matching fraction

This calculator uses a continued-fraction algorithm — the same method used to find the best small-denominator approximation to any decimal, which is how 0.75 resolves cleanly to 3/4 instead of 75/100.

Where it's genuinely useful

Woodworking and cooking measurements are usually expressed in fractions (⅜ inch, ⅔ cup), while calculators and spreadsheets output decimals — this bridges the two.

Frequently asked questions

I measured 0.375 inches on a caliper — what drill bit size is that?

0.375 = 375/1000. Simplify by dividing both by 125: 3/8. So you need a 3/8-inch drill bit. The calculator finds this instantly and shows the GCD reduction step.

How does this handle repeating decimals like 0.333…?

The continued-fraction algorithm finds the best rational approximation. For 0.333… it returns 1/3. For 0.142857142857… it returns 1/7. Enter enough decimal places for the algorithm to detect the repeating pattern.

What's the difference between this and the fraction-to-decimal converter?

This tool goes decimal → fraction (0.75 → 3/4). The fraction-to-decimal converter goes the other direction (3/4 → 0.75). They're inverse operations — use whichever direction your problem needs.