Decimal to Fraction Calculator

A decimal to fraction calculator converts any decimal number into its equivalent fraction, reduced to lowest terms. Enter a decimal like 0.75 and get 3/4. Enter 0.125 and get 1/8. It handles both terminating decimals (like 0.625) and repeating decimals (like 0.333...), showing the step-by-step simplification process.

This conversion is fundamental to mathematics because fractions and decimals are two representations of the same values, but each is more convenient in different contexts. Fractions are exact and easier to work with in algebra, while decimals are better for measurement and comparison. Being able to move fluently between the two is an essential skill.

• Math homework - Converting decimal answers back to fractions for exact representation
• Cooking and recipes - Translating digital scale readings (0.375 lbs) into measuring cup fractions (3/8)
• Construction - Converting decimal inches from digital tools to fractional inches for standard lumber and hardware
• Finance - Expressing interest rates and ratios as exact fractions for contracts and legal documents
• Science and engineering - Converting measured decimals to fractions for algebraic manipulation
• Music - Relating decimal time signatures or beat divisions to standard fractional notation

• Repeating decimals require algebraic tricks - Converting 0.1666... to 1/6 involves setting up an equation, not just moving the decimal point. Many students don't know the technique
• Simplification requires finding the GCF - Once you have a fraction like 375/1000, you need to find that both divide by 125 to get 3/8
• Not all decimals terminate - Irrational numbers like pi (3.14159...) cannot be expressed as exact fractions. Knowing which decimals have fraction equivalents requires understanding rational vs. irrational numbers
• Large denominators look intimidating - A decimal like 0.0625 produces 625/10000 before simplification. Recognizing that this simplifies neatly to 1/16 takes practice

For terminating decimals, count the digits after the decimal point. That tells you the denominator: 1 digit means tenths, 2 digits means hundredths, 3 digits means thousandths, and so on. Write the digits as the numerator over that denominator, then simplify. For 0.45: 45/100 = 9/20 (divide both by 5).

For repeating decimals, use algebra. Let x = 0.333..., then 10x = 3.333..., and subtracting gives 9x = 3, so x = 3/9 = 1/3. For decimals with a non-repeating part followed by a repeating part (like 0.1666...), the technique is similar but requires multiplying by different powers of 10 to align the repeating sections.

Example

Convert 0.875 to a fraction. The decimal has 3 digits after the point, so write 875/1000. Find the GCF of 875 and 1000: both are divisible by 125. So 875/125 = 7 and 1000/125 = 8. The fraction is 7/8. Verify: 7 divided by 8 = 0.875.

• 0.5 - Equals 5/10, simplifies to 1/2
• 0.75 - Equals 75/100, simplifies to 3/4 (divide by 25)
• 0.333... - Repeating decimal that equals exactly 1/3
• 0.625 - Equals 625/1000, simplifies to 5/8 (divide by 125)
• 0.1666... - Equals 1/6 (non-repeating "1" followed by repeating "6")

• Get exact fractions instantly - No need to manually count decimal places, compute GCFs, and simplify step by step
• Handle repeating decimals correctly - The algebraic method for converting repeaters is automated, avoiding the most error-prone conversion type
• Always get lowest terms - The result is fully simplified so you never end up with a reducible fraction
• See the step-by-step process - Follow the conversion logic to learn and verify the method
• Work confidently between representations - Switch between decimals and fractions without second-guessing accuracy

How do I convert a terminating decimal to a fraction?

Count the decimal places to determine the denominator. One decimal place means tenths, two means hundredths, three means thousandths. Write the number without the decimal as the numerator, then simplify. For 0.35: 35/100. GCF(35, 100) = 5. Result: 7/20.

How do I convert a repeating decimal to a fraction?

Use algebra. For 0.272727... (repeating "27"), let x = 0.272727..., then 100x = 27.272727.... Subtract: 99x = 27, so x = 27/99 = 3/11. The number of 9s in the denominator matches the length of the repeating block. A two-digit repeat uses 99, a three-digit repeat uses 999, and so on.

Can every decimal be converted to a fraction?

No. Only rational numbers can be expressed as fractions. Terminating and repeating decimals are rational. Non-repeating, non-terminating decimals like pi (3.14159265...) and the square root of 2 (1.41421356...) are irrational and have no exact fraction equivalent. You can approximate them (pi is approximately 22/7), but the fraction is never exact.

What is the fastest way to simplify a fraction?

Find the GCF (Greatest Common Factor) of the numerator and denominator and divide both by it. For 120/180: GCF is 60, giving 2/3. If you cannot spot the GCF immediately, start by dividing both by small primes (2, 3, 5) repeatedly until neither can be divided further.

Why does 0.999... equal 1?

This is a famous result in mathematics. Let x = 0.999..., then 10x = 9.999..., and subtracting gives 9x = 9, so x = 1. It is not "approaching" 1 or "almost" 1. The repeating decimal 0.999... is exactly, provably equal to the integer 1. This also means 1/3 = 0.333... and 3 x (1/3) = 3 x 0.333... = 0.999... = 1.

How do I convert a mixed decimal like 2.75 to a fraction?

Separate the whole number and the decimal part. Convert the decimal: 0.75 = 75/100 = 3/4. Combine with the whole number to get the mixed number 2 3/4, or convert to an improper fraction: (2 x 4 + 3) / 4 = 11/4. This approach works for any decimal with a whole number part.