Fraction / Decimal / Percent Converter
Convert between fractions, decimals, and percentages in any direction. Six conversion modes in one tool.
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How to use this calculator
- 1
Select the conversion direction from the dropdown.
- 2
Enter the numerator (or decimal/percent value) in the first field.
- 3
For fraction modes, also enter the denominator.
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The converted value is shown immediately, along with all three forms (fraction, decimal, percent).
Frequently asked questions
How do you convert a fraction to a percent?
Divide the numerator by the denominator to get a decimal, then multiply by 100. For 3/4: 3 ÷ 4 = 0.75; 0.75 × 100 = 75%. Alternatively, scale the fraction to a denominator of 100: 3/4 = 75/100 = 75%.
How do you convert a decimal to a fraction?
Write the decimal over 1, then multiply numerator and denominator by 10 for each decimal place. For 0.75: 0.75/1 × 100/100 = 75/100. Simplify using GCD: GCD(75,100)=25, so 75/100 = 3/4. For repeating decimals (e.g., 0.333…), use the formula n = repeating block / (9s matching block length): 0.333… = 3/9 = 1/3.
What percent is 1/3?
1/3 = 0.33333… = 33.333…% (a repeating decimal that cannot be expressed exactly in finite decimal form). Similarly, 2/3 ≈ 66.667% and 1/7 ≈ 14.286%. These repeating decimals are exact fractions but approximations as percents.
Why do fractions and percentages both represent parts of a whole?
Percent literally means "per hundred" (Latin per centum). So 75% = 75/100 = 3/4. Both fractions and percents express parts of a whole; percents standardize the denominator to 100 for easy comparison. 60% vs 3/5 vs 0.6 are all the same value in three equivalent notations.
Fraction, decimal, and percent converter — all six directions
Three equivalent representations
Every rational number can be written as a fraction (p/q), a decimal (terminating or repeating), and a percent (decimal × 100). These are not different quantities but different notations for the same value. Converting between them is a core arithmetic skill: 0.25 = 1/4 = 25% all represent "one quarter of the whole." Understanding which form is most useful for a given context — fractions for exact arithmetic, decimals for computation, percents for communication — is a key mathematical literacy skill.
Terminating vs. repeating decimals
A fraction p/q (in lowest terms) has a terminating decimal if and only if q has no prime factors other than 2 and 5. If q = 4 = 2², then 1/4 = 0.25 (terminates). If q = 3, then 1/3 = 0.333… (repeats). If q = 6 = 2×3, then 1/6 = 0.1666… (repeats). This rule predicts which fractions produce clean decimals — 1/8, 1/16, 1/25, 1/32 all terminate; 1/3, 1/7, 1/11 all repeat.
Practical applications of all three forms
Test scores are reported as percentages (75%) for easy comparison but computed as fractions (45/60) in the classroom. Financial returns are percentages (7% annually), but compound interest requires the decimal form (1.07^n). Probability is most naturally a fraction (3/10 chance) but is expressed as percent (30%) in public communication. Having fluency in all three representations allows you to move between them as different situations demand.
Learn more from an authoritative source:
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