Fraction to Decimal Calculator
Our free basic math calculator solves fraction decimal problems. Get worked examples, visual aids, and downloadable results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Decimal = Numerator / Denominator
Where the numerator is the top number of the fraction and the denominator is the bottom number. For mixed numbers, add the whole number to the fraction's decimal value. The result is terminating if the simplified denominator's only prime factors are 2 and 5, otherwise it repeats.
Worked Examples
Example 1: Simple Fraction Conversion
Problem:Convert 3/8 to a decimal and percentage.
Solution:Division: 3 / 8 = 0.375\nVerification: 0.375 x 8 = 3.000 (correct)\nPercentage: 0.375 x 100 = 37.5%\nSimplification check: GCD(3,8) = 1, already simplified\nDenominator factors: 8 = 2^3 (only factor of 2)\nTherefore: terminating decimal
Result:3/8 = 0.375 = 37.5% (terminating decimal)
Example 2: Mixed Number with Repeating Decimal
Problem:Convert 2 and 5/6 to a decimal.
Solution:Fraction part: 5 / 6 = 0.8333...\nLong division: 50 / 6 = 8 remainder 2\n20 / 6 = 3 remainder 2 (repeating)\nRepeating pattern: 3\nDecimal: 0.8333... = 0.83(3)\nMixed number: 2 + 0.8333... = 2.8333...\nPercentage: 2.8333... x 100 = 283.33%
Result:2 5/6 = 2.8333... = 2.83(3) = 283.33%
Frequently Asked Questions
How do you convert a fraction to a decimal number?
Converting a fraction to a decimal is straightforward: simply divide the numerator (top number) by the denominator (bottom number). For example, to convert 3/4 to a decimal, divide 3 by 4, which equals 0.75. For mixed numbers like 2 and 3/4, first convert the fraction part to a decimal (3 divided by 4 equals 0.75) and then add it to the whole number to get 2.75. You can perform this division by hand using long division, or use a calculator for quick results. Some fractions produce terminating decimals like 1/4 = 0.25, while others produce repeating decimals like 1/3 = 0.333... that go on forever in a repeating pattern.
How do you simplify a fraction to its lowest terms?
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both numbers by the GCD. The GCD is the largest number that divides evenly into both the numerator and denominator. For example, to simplify 12/18, the GCD of 12 and 18 is 6, so divide both by 6 to get 2/3. You can find the GCD using the Euclidean algorithm (repeatedly dividing the larger number by the smaller and taking the remainder) or by listing the factors of each number. A fraction is in its simplest form when the only common factor of the numerator and denominator is 1, meaning no further reduction is possible.
How do you convert a repeating decimal back to a fraction?
To convert a repeating decimal to a fraction, use algebra by setting the decimal equal to a variable, then creating an equation that eliminates the repeating part. For 0.333..., let x = 0.333..., then 10x = 3.333..., and subtracting gives 9x = 3, so x = 3/9 = 1/3. For decimals with non-repeating parts before the repeating section, like 0.1666..., let x = 0.1666..., then 10x = 1.666..., 100x = 16.666..., subtracting gives 90x = 15, so x = 15/90 = 1/6. The number of digits in the repeating block determines the multiplier: one repeating digit uses 9, two repeating digits use 99, three use 999, and so on.
What are the most common fraction to decimal conversions to memorize?
The most useful fraction-decimal equivalents to memorize include the basic halves, quarters, eighths, thirds, and fifths. Key conversions are 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/3 = 0.333, 2/3 = 0.667, 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, and 7/8 = 0.875. For sixths: 1/6 = 0.1667 and 5/6 = 0.8333. Knowing these common conversions allows you to quickly estimate calculations, check work, and convert between forms without a calculator. They are especially useful in cooking, woodworking, and other practical applications where measurements are given in fractional inches.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy