The formula this page uses
0.d₁d₂…dₙ = (the digits as a whole number) / 10ⁿ, then divide top and bottom by their GCF
Convert decimals to fractions, with steps
Use the free decimal to fraction calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Decimal to Fraction Calculator explained
The short version
- Count the decimal places, write the digits over that many zeros after a 1, then reduce.
- 0.72 has two places, so it starts life as 72/100 and tidies up to 18/25.
- A repeating decimal needs a different trick: multiply, subtract, and the repeat cancels itself out.
What each part means
SymbolWhat it means
n — Number of decimal placesHow many digits sit after the point. It decides how many zeros go on the bottom.
10ⁿ — The starting denominator10 for one place, 100 for two, 1000 for three, and so on.
GCF — Greatest common factorWhat you divide the top and bottom by to reach lowest terms.
x — The unknown in the repeating trickSet x equal to the repeating decimal, then multiply it by a power of ten.
Show your work: a full example
- Convert 0.72 to a fraction0.72
- Count the decimal places2 places, so the bottom is 10² = 100
- Write the digits over 10072/100
- Find the greatest common factorGCF(72, 100) = 4
- Divide both by 472 ÷ 4 = 18 and 100 ÷ 4 = 25
- Write the answer0.72 = 18/25
- Check by dividing back18 ÷ 25 = 0.72
A second, different case
- A different case: the decimal repeats forever0.4444…
- Name itlet x = 0.4444…
- Multiply by 10 to shift one repeat10x = 4.4444…
- Subtract the first line from the second10x − x = 4.4444… − 0.4444…
- The endless tails cancel9x = 4, so x = 4/9
- Try a two-digit repeat, 0.363636…100x − x = 36, so 99x = 36
- Reduce it36/99 = 4/11, and 4 ÷ 11 = 0.363636…
Copy-ready example
0.72
Convert 0.72 to a fraction
Questions about the Decimal to Fraction Calculator
How can I tell in advance whether a decimal will ever stop?
Look at the fraction it came from once it is in lowest terms. If the bottom number is built only from 2s and 5s, the decimal stops, because our place values are tenths, hundredths and thousandths. Any other prime on the bottom, such as 3 or 7, makes it repeat forever.
What do I do with a number like 3.4 that has a whole part?
Leave the 3 alone and convert only the 0.4, which is 4/10 = 2/5. So 3.4 is 3 and 2/5. If you need it as a single improper fraction, multiply the whole by the bottom and add: 3 × 5 + 2 = 17, giving 17/5.
Why does multiplying by 10 make a repeating decimal solvable?
Because the tail after the point is identical in both lines. Subtracting lines up 0.4444… against 4.4444… and the endless part vanishes completely, leaving an ordinary equation with whole numbers. For a two-digit repeat you multiply by 100 instead, so that the tails still match.
Is 0.999… really equal to 1?
Yes. Run the same trick: let x = 0.999…, so 10x = 9.999…, and subtracting gives 9x = 9, which means x = 1. They are two spellings of the same number, not two numbers that are almost equal.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.