Fractions and decimals are two languages for the same numbers. A fraction like 3/4 and a decimal like 0.75 say exactly the same thing about exactly the same quantity — they just look different. Knowing how to switch between the two fluently is one of the most useful math skills you can have.
Fractions to decimals: just divide
A fraction is a division problem in disguise. The numerator divides by the denominator. So 3/4 = 3 ÷ 4 = 0.75.
You can do this by long division, by calculator, or by recognition for common fractions. Worth memorizing:
- 1/2 = 0.5
- 1/4 = 0.25, 3/4 = 0.75
- 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8
- 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875
- 1/10 = 0.1, 1/100 = 0.01, 1/1000 = 0.001
Terminating vs repeating decimals
Some fractions give a clean decimal that ends; others give a decimal that repeats forever. Which you get depends entirely on the denominator.
A fraction (in lowest terms) terminates if and only if its denominator, after factoring, contains only 2s and 5s. So 3/8 terminates because 8 = 2³. And 7/20 terminates because 20 = 2² × 5. But 1/3 repeats (denominator has a 3), 1/6 repeats (2 × 3), and 1/7 repeats (7).
Handling repeating decimals
Repeating decimals are written with a bar over the repeating block:
- 1/3 = 0.333... = 0.3̄
- 2/3 = 0.666... = 0.6̄
- 1/6 = 0.1666... = 0.16̄
- 1/7 = 0.142857142857... = 0.1̄4̄2̄8̄5̄7̄
- 1/9 = 0.1̄, 1/11 = 0.0̄9̄
In practice, round to as many decimal places as the task needs. Two decimal places is standard for money. Four is typical for scientific work.
Decimals to fractions: read it out loud
Any terminating decimal converts with a simple rule: read it in words, write the words as a fraction, simplify.
Example 1: 0.75 is "seventy-five hundredths" = 75/100 = 3/4.
Example 2: 0.125 is "one hundred twenty-five thousandths" = 125/1000 = 1/8.
Example 3: 2.4 is "two and four tenths" = 2 + 4/10 = 2 + 2/5 = 12/5.
Converting repeating decimals to fractions
This one feels like magic but it is just algebra. For a decimal with a single repeating digit, like 0.3̄:
- Let x = 0.3̄.
- Multiply both sides by 10: 10x = 3.3̄.
- Subtract the first from the second: 10x − x = 3.3̄ − 0.3̄, so 9x = 3.
- Solve: x = 3/9 = 1/3.
For a two-digit repeat like 0.2̄7̄, multiply by 100 instead. For a three-digit repeat, multiply by 1000. The rule: if n digits repeat, multiply by 10ⁿ.
Decimals to percents (and fractions to percents)
To convert a decimal to a percent, multiply by 100 (or just shift the decimal two places right): 0.45 = 45%. To go from percent to decimal, divide by 100: 12% = 0.12.
Fraction to percent: convert the fraction to a decimal first, then to a percent. 3/8 = 0.375 = 37.5%.
When to use which form
Use fractions for: exact ratios, recipes (1/3 cup is cleaner than 0.333 cup), probability in simple events (1/6 for a die), carpentry measurements (3/16 inch).
Use decimals for: money (always), calculations involving a mix of numbers, measurements expressed in a metric or decimal system, inputs to computers and calculators.
Use percents for: comparisons (interest rates, discounts, tax), statistics that will be shared with non-technical readers.
Common trouble spots
Rounding 2/3 to 0.67 and then using that number in a chain of calculations can propagate error. Keep the exact fraction as long as possible; convert only at the final step.
Do not confuse 0.5 (one-half) with 0.05 (one-twentieth). Two decimal places can make a ten-times difference. Write a zero before the decimal point in small numbers to make them clearer: 0.5 is easier to read than .5.
Mixed numbers and improper fractions
A mixed number like 2 3/4 combines a whole number and a proper fraction. The improper-fraction form is 11/4 (because 2 × 4 = 8, plus 3 = 11). Both are equal; both are valid. Calculators and spreadsheets prefer improper fractions or decimals. Recipes, construction specs, and everyday conversation prefer mixed numbers because they're easier to visualize. "Two-and-a-quarter cups" is immediately meaningful in a way that "9/4 cups" is not.
To convert a mixed number to a decimal: handle the whole and the fraction separately, then add. 3 5/8 → 3 + 0.625 = 3.625. To convert a decimal to a mixed number: the integer part is the whole number; the decimal part converts via the read-aloud rule. 3.625 → 3 and 625/1000 → 3 and 5/8.
Equivalent fractions and the reason simplification matters
2/4, 3/6, 50/100, and 0.5 are all the same quantity. Which form you choose changes nothing mathematically, but it changes everything about how easily a human can read it. 2/4 looks awkward; 1/2 looks clean. In test answers, math teachers almost universally expect the simplified form because it's the canonical representation — an unreduced answer reads as incomplete work, even when correct.
To simplify: find the greatest common divisor (GCD) of numerator and denominator and divide both by it. 30/45: GCD is 15, giving 2/3. When the GCD isn't obvious, repeatedly divide by small primes (2, 3, 5, 7) until nothing divides cleanly anymore.
Why certain denominators appear so often
Some fractions feel natural — halves, quarters, eighths, tenths — while others feel awkward. That's not random. Fractions whose denominators are factors of 10 (1/2, 1/5, 1/10) convert to clean decimals because our number system is base 10. Fractions whose denominators are powers of 2 (1/2, 1/4, 1/8, 1/16) dominate carpentry and engineering because repeated halving is how rulers and drill-bit sets are designed. Fractions with denominators 3, 7, or 11 are useful mathematically but never terminate in decimal — which is why we say "a third of the class" but almost never write 0.3333333 in anything but a spreadsheet cell.
Make it instant
Our fraction calculator converts between fractions, decimals, and mixed numbers in both directions, showing the work as it goes. Use it to check homework, to prep for exams, or just to avoid reaching for long division. Fluency in both forms unlocks everything from algebra to financial planning.