How to convert a decimal to a fraction by hand
The place-value method, reducing with the greatest common divisor, mixed numbers, negatives, and why repeating decimals need a different approach.
Start with place value
Every terminating decimal is already a fraction hiding in plain sight. The digits after the point tell you the denominator: one place means tenths, two means hundredths, three means thousandths, and so on. So 0.75 is 75 hundredths, written 75/100, and 0.125 is 125 thousandths, written 125/1000. The numerator is simply the decimal digits read as a whole number. This is exactly the first step the tool performs before it reduces anything.
Reduce with the greatest common divisor
A raw fraction like 75/100 is correct but not in lowest terms. To simplify, find the greatest common divisor of the numerator and denominator, the largest number that divides both evenly, then divide each by it. For 75 and 100 the greatest common divisor is 25, so both drop to 3/4. When no common factor above one remains, the fraction is fully reduced. The tool uses the Euclidean algorithm to do this instantly, which is why every answer it gives is already simplified.
Mixed numbers and negatives
When a decimal is bigger than one, the improper fraction can be split into a whole part and a remainder. Take 2.5, which is 5/2: two goes into five twice with one left over, giving the mixed number 2 1/2. Negative decimals follow the same steps with the sign carried on the numerator, so -0.6 becomes -3/5. The tool shows the mixed or whole form next to the simplified fraction so you can pick whichever reads best for your work.
Where the method breaks down
Place value only works cleanly for decimals that stop. Repeating decimals such as 0.3333... never terminate, so reading a fixed number of digits only approximates them. Typing 0.3333 yields 3333/10000, which is near 1/3 but not equal to it. The exact repeating-decimal method uses algebra: set x equal to the decimal, multiply by a power of ten, and subtract to cancel the repeating tail. For everyday terminating values, though, the place-value approach above is all you need.