A clear answer before the details
Write a terminating decimal over a power of 10, then divide both parts by their greatest common factor. Repeating decimals use an algebraic subtraction step to remove the repeating tail.
How a decimal fraction converter finds an exact value
A decimal fraction converter writes the digits over the correct power of ten and then reduces the result. For 0.625, write 625/1000, divide both parts by 125, and get 5/8. The decimal to fraction with steps view makes the place-value denominator and greatest common factor visible, which helps students check each transformation rather than memorising a shortcut.
Terminating and repeating decimal forms
Terminating decimals have a finite number of digits and can always be written over 10, 100, 1,000, or another power of ten. A repeating decimal to fraction conversion uses a second equation: multiply by a power of ten, subtract the original repeating expression, and solve for x. For example, 0.333… becomes 3x − x = 0.999… − 0.333…, so x = 1/3. Use the exact fraction whenever rounding would affect a later answer.
Formula guide
The key equations are separated below. Start with the calculator mode, then choose the shape or model that matches your problem.
Place value
Use a power of 10 that matches the number of decimal places.
Simplify
g is the greatest common factor of numerator and denominator.
Repeating decimal
For a repeating block, subtract shifted copies to remove the repeat.
Worked example
The decimal 1.625 becomes 1625/1000. Dividing numerator and denominator by 125 gives 13/8, or 1 5/8.
Formulas for common use cases
Use the matching equation for the problem you are solving, then enter its variables in the calculator above.
Terminating decimal
Reduce the place-value fraction to an exact answer.
Repeating decimal
Set x equal to the repeat, shift it, subtract, and solve.
Mixed number
Divide the numerator by the denominator for a mixed-number form.
How to use this calculator
- Enter a decimal such as 1.625 or -0.75.
- Use repeating mode when a digit block repeats forever.
- Read the simplified fraction and optional mixed number.
- Copy or share the exact conversion.
Where it helps
Fraction form is valuable in algebra, ratios, recipes, measurements, and any setting where an exact value is safer than a rounded decimal. The result keeps the sign in a standard position and explains each reduction so the conversion can be checked by hand.
Common mistakes
Do not enter a rounded approximation when you need an exact repeating fraction. A trailing zero does not change a decimal’s value, but it does change the power of 10 used in the first unsimplified fraction. Always verify the final fraction by dividing it back into a decimal.