Fraction to decimal: the division hiding in every fraction
A fraction is not a special kind of number. It is a division that nobody has carried out yet. The bar between the two numbers is the divide sign, so 3/8 is a shorter way of writing 3 ÷ 8, and doing that division is all there is to converting it.
The method
Decimal = numerator ÷ denominator. To get the percentage, multiply the decimal by 100. That is the whole procedure; there is no second rule for "hard" fractions.
A real example: 3/8
- Divide:
3 ÷ 8 = 0.375. - To a percentage:
0.375 × 100 = 37.5%.
So three-eighths is 0.375, or 37.5%. All three notations are the same quantity written three ways, and none is more precise than another here.
Why bother: comparing fractions
This is where the conversion earns its keep. Is 5/8 bigger than 3/5? Staring at them does not settle it, because the two have different denominators and your intuition has nothing to anchor to. Convert both:
5 ÷ 8 = 0.6253 ÷ 5 = 0.6
0.625 is larger, so 5/8 wins — by 0.025, which is one fortieth. The traditional method is to find a common denominator (40ths: 25/40 against 24/40), and that works too. Converting to decimals is simply faster when you only want to know which is bigger, and it scales to comparing five things at once, where common denominators become miserable.
A real example: 7/16 on a tape measure
7 ÷ 16 = 0.4375, or 43.75%. Imperial tape measures are marked in sixteenths, so this is the conversion that turns a measurement into something a calculator, a spreadsheet or a cutting list can use. Just under seven-sixteenths of an inch is just under 0.44 of an inch — and now it can be added to a decimal figure without a second thought.
When the decimal never ends
Some fractions do not convert to a tidy decimal. 1 ÷ 3 = 0.333333..., repeating forever. The fraction 1/3 is the exact value; 0.333333 is an approximation that has been cut off somewhere.
This matters more than it looks. Add 1/3 three times and you get exactly 1. Add 0.333333 three times and you get 0.999999 — close, but not the same number, and the gap grows every time you repeat the operation. If you are going to do further arithmetic, keep the fraction as long as you can and convert at the end. Convert first and you have baked a rounding error into every step that follows.
A fraction terminates in decimal form only when its denominator's prime factors are just 2s and 5s — which is why eighths (2×2×2), sixteenths and fifths all come out clean, and why thirds, sevenths and ninths never do.
What about a denominator of zero
There isn't an answer. Dividing by zero is not a very large number or a very small one; it is undefined, because no number multiplied by zero gives you anything other than zero. A calculator that returns a huge figure there has misled you. The tool below shows the infinity symbol rather than a number, which is at least honest about there being nothing to report.
Run your own numbers
The free Fraction → Decimal converter does the division and the percentage together, entirely on your device. If you also want the fraction reduced to its simplest form first, the GCD & LCM calculator finds the number to divide both halves by.