Fractions, decimals and percents
A fraction, a decimal and a percent can all name the exact same value — 1/4, 0.25 and 25% are three ways to write one quarter. Converting between them is division and scaling, not a different kind of math each time. The calculators below handle each direction; this page explains how they connect.
The three forms, and how they relate
A fraction is a numerator over a denominator — the number of parts you have, over the number of equal parts the whole was split into. 3/4 means three of four equal parts.
A decimal writes that same value using place value instead of two separate numbers. 3/4 and 0.75 are the same amount, just counted differently.
A percent means per hundred — the value rescaled so the whole is always 100, whatever the original denominator was. 75% and 3/4 are that same amount again, on a different scale.
None of the three is more exact than the others. Which one to write depends on what happens next with it.
Converting between them
Six directions in total. Two have a calculator below; the method for each is the same either way.
| From | To | Method |
|---|---|---|
| Fraction | Decimal | Divide the numerator by the denominator. Fraction to decimal calculator |
| Fraction | Percent | Divide, then multiply by 100. Fraction to percent calculator |
| Decimal | Fraction | Write the decimal over the matching power of 10, then simplify. |
| Decimal | Percent | Multiply by 100 — shift the decimal point two places right. |
| Percent | Fraction | Write the percent over 100, then simplify. |
| Percent | Decimal | Divide by 100 — shift the decimal point two places left. |
Each method above is a short, fixed sequence — divide, then scale, never the other way around. That's the same idea behind evaluating a longer expression: the order of operations calculator breaks down any typed expression the same way, one step at a time, in the order it has to happen.
Common values in all three forms
The same set of fractions, side by side in every form.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | zero point three recurring | 33.(3)% |
| 2/3 | zero point six recurring | 66.(6)% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | zero point one six recurring | 16.(6)% |
| 1/8 | 0.125 | 12.5% |
When to use which form
Fractions are the clearest form for exact parts of a whole — a recipe, a measurement, a probability. They stay exact; nothing gets rounded.
Decimals are the natural form for a calculation, especially one involving money or measurement, because they combine with ordinary arithmetic without an extra conversion step first.
Percents are the clearest form for comparison — a discount, a test score, a growth rate. Rescaling everything to a common denominator of 100 is exactly what makes two different quantities comparable at a glance.
The calculators
- Fraction to decimal calculator — divides a fraction out exactly, repeating decimals included.
- Fraction to percent calculator — divides, then scales the result to a per-hundred figure.
Frequently asked questions
Are a fraction, a decimal and a percent ever exactly the same number?
They represent the exact same value, written three different ways — 1/4, 0.25 and 25% all name one quarter. None is more "correct" than the others; which one to use depends on what you're doing with it.
Why does converting a fraction to a percent mean multiplying by 100?
Percent means per hundred. Multiplying by 100 rescales a value measured out of 1 into a value measured out of 100 — the same quantity, on a different scale, not a new calculation.
Why do some fractions convert to decimals that never end?
A fraction's decimal terminates only when its denominator, once simplified, has no prime factors besides 2 and 5. Any other factor — a 3, a 7 — forces the division into a repeating pattern that never reaches a remainder of zero.
Do I need to simplify a fraction before converting it?
No — dividing 2/8 gives the same 0.25 that dividing the simplified 1/4 does. Simplifying first can make the division easier by hand, but it doesn't change the answer either calculator gives.
Which form should I use for a discount or a test score?
Percent — it's built for comparing a part to a whole out of a common scale of 100, which is exactly what a discount or a score is doing.