Convert
5 tools for convert operations.
About Fraction Conversion Tools
Fractions, decimals, percentages, and ratios are four different ways to express the same numerical relationship. Converting between them is a fundamental math skill used in cooking, finance, science, and everyday calculations. Our conversion tools handle all five common conversions instantly with clear formulas so you can understand the underlying math, not just the answer.
Fraction to Decimal
Converting a fraction to a decimal is straightforward: divide the numerator by the denominator. For example, 3/4 = 3 รท 4 = 0.75. Some fractions produce terminating decimals (1/4 = 0.25), while others produce repeating decimals (1/3 = 0.3333... = 0.3ฬ). Fractions whose denominators have only factors of 2 and 5 always terminate; all others repeat. The Fraction to Decimal tool shows both the decimal value and whether it terminates or repeats.
Decimal to Fraction
To convert a terminating decimal to a fraction, write the decimal digits as the numerator over the appropriate power of 10 as the denominator, then simplify. For example, 0.75 = 75/100 = 3/4. For repeating decimals, the conversion requires algebra: let x = 0.3333..., then 10x = 3.333..., subtracting gives 9x = 3, so x = 3/9 = 1/3. The Decimal to Fraction tool handles both terminating and repeating decimals automatically.
Fraction to Percentage and Back
A percentage is simply a fraction with denominator 100. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/8 = 0.375 ร 100 = 37.5%. To convert a percentage back to a fraction, write the percentage over 100 and simplify: 37.5% = 37.5/100 = 375/1000 = 3/8. The Fraction to Percentage and Percentage to Fraction tools show this process step by step.
Ratio to Fraction
A ratio like 3:5 means "3 parts to 5 parts." To express the first quantity as a fraction of the total, write 3/(3+5) = 3/8. To express it as a fraction of the second quantity, write 3/5. The Ratio to Fraction tool handles both interpretations and simplifies the result to lowest terms.
Frequently Asked Questions
Is 0.666... exactly equal to 2/3?
Yes. The repeating decimal 0.666... (written as 0.6ฬ) is exactly equal to 2/3, not approximately. This can be proven algebraically: let x = 0.666..., then 10x = 6.666..., subtracting gives 9x = 6, so x = 6/9 = 2/3.
How do you convert 1.25 to a fraction?
Write 1.25 as 125/100 (multiply numerator and denominator by 100 to remove the decimal), then simplify by dividing by GCD(125,100) = 25: 125/100 = 5/4 = 1 1/4.
What is 3/7 as a percentage?
3 รท 7 = 0.42857..., multiplied by 100 = 42.857...%, usually rounded to 42.86%.