What this converter does
Fractions, decimals, and percentages are three ways of writing the same value. This 3-way converter takes a fraction a/b and instantly shows the equivalent decimal and percentage, so you can move between the formats without manual long division.
How to use it
Enter the numerator (the top number, a) and the denominator (the bottom number, b). The calculator divides a by b to produce the decimal, then multiplies that decimal by 100 to produce the percent. Both results update together.
The formula explained
The core relationship is simple: a fraction is just a division problem. \(\text{decimal} = a \div b\). To turn the decimal into a percentage you scale it to "parts per hundred": \(\text{percent} = \text{decimal} \times 100\). Reversing the process, a percent divided by 100 gives the decimal, and any terminating decimal can be written as a fraction over a power of ten.
$$\text{Decimal} = \frac{\text{Numerator }(a)}{\text{Denominator }(b)} \qquad \text{Percent} = \frac{\text{Numerator }(a)}{\text{Denominator }(b)} \times 100\%$$
Worked example
Take the fraction 3/4. Dividing gives \(3 \div 4 = \mathbf{0.75}\). Multiplying by 100 gives \(0.75 \times 100 = \mathbf{75\%}\). So 3/4, 0.75, and 75% are all the same quantity.
Another: \(5/8 = 0.625 = 62.5\%\).
FAQ
What if the denominator is 0? Division by zero is undefined, so the converter returns 0 for that case — enter a non-zero denominator for a meaningful result.
Can I enter improper fractions? Yes. For example 5/4 gives 1.25 and 125%, which is perfectly valid.
How do I convert a percent back to a fraction? Put the percent over 100 and simplify — for instance \(75\% = 75/100 = 3/4\).
