mathsolvers.io
Converters

Decimal to Fraction

Convert any decimal — including recurring ones like 0.333… — to a simplified fraction, with full step-by-step working.

Common decimals — click to convert

Step-by-step solution

Enter a decimal and press Convert to see the working

Terminating decimals

Multiply by 10 for each decimal place to remove the point, then simplify using the GCD.

0.625 → 625/1000 → 5/8

Recurring decimals

Use algebra — let x = the decimal, multiply to shift one full repeat, then subtract to cancel it.

0.333… → 9x = 3 → x = 3/9 → 1/3

Examples

0.5 → 1/2 A simple terminating decimal, easily converted and simplified.
0.75 → 3/4 A terminating decimal requiring simplification after initial conversion.
1.25 → 1 1/4 A terminating decimal greater than 1, shown as a mixed number.
0.333... → 1/3 A basic recurring decimal, demonstrating the algebraic conversion method.
0.1666... → 1/6 A recurring decimal with a non-recurring part before the repeating digits.
2.121212... → 2 4/33 A recurring decimal greater than 1, converted to a mixed number.
0.142857142857... → 1/7 A recurring decimal with a long repeating block of digits.
0.0625 → 1/16 A terminating decimal with several decimal places, showing power of 10 and simplification.

Decimal to Fraction Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

When you'd actually need this

A recipe calls for 0.75 cup of butter — that's exactly ¾ cup, which is a real measuring cup marker. A calculator shows 0.333... when you divide 1 by 3, but the exact answer is ⅓. A ruler reads 0.5 inches — that's the ½-inch mark. Converting decimals to fractions lets you use exact values instead of rounded approximations.

Worked example

"Convert 0.625 to a fraction."

Step 1: 3 decimal places → multiply by 1000

Step 2: 0.625 = 625/1000

Step 3: GCD(625, 1000) = 125

Step 4: 625 ÷ 125 = 5, 1000 ÷ 125 = 8

Result: 5/8

Verify: 5 ÷ 8 = 0.625 ✓

Common mistake to avoid

  • ✗ Treating 0.333 as equal to ⅓: 0.333 is a rounded approximation. The recurring decimal 0.333... (with the 3 repeating forever) equals ⅓ exactly — use the algebraic method for recurring decimals to get the precise fraction.
About

Decimal to Fraction Converter

Our Decimal to Fraction Converter is a powerful tool designed to help GCSE Maths and KS3 students understand how to convert both terminating and recurring decimals into their simplest fractional forms. Whether you're dealing with a straightforward decimal like 0.75 or a more complex recurring decimal such as 0.333..., this converter provides clear, step-by-step working.

For terminating decimals, the converter demonstrates how to multiply by a power of 10 to remove the decimal point, then simplifies the resulting fraction using the Greatest Common Divisor (GCD) method, often showing the Euclidean algorithm. For recurring decimals, it employs the algebraic method (e.g., letting x = 0.333..., multiplying by 10, and subtracting to eliminate the recurring part). Values greater than 1 are presented as mixed numbers (e.g., 1.25 becomes 1 1/4), and every answer is verified by dividing the numerator by the denominator, ensuring accuracy and building confidence in your understanding.

Common mistakes to avoid

  • Converting 0.125 to 125/100:The denominator is incorrect. The last digit '5' is in the thousandths place, so the denominator should be 1000, not 100. 0.125 = 125/1000, which simplifies to 1/8.
  • Leaving 0.5 as 5/10:The fraction is not in its simplest form. Both the numerator and denominator can be divided by a common factor (5). 0.5 = 5/10, which simplifies to 1/2.
  • For 0.1232323..., setting x = 0.12323... and 10x = 1.2323..., then subtracting 10x - x to get 9x = 1.11:The recurring parts do not align correctly for subtraction. You need to multiply by powers of 10 that make the recurring parts line up perfectly. For 0.1232323..., let x = 0.12323... Then 10x = 1.2323... and 1000x = 123.2323... Subtracting 1000x - 10x gives 990x = 122, so x = 122/990.
  • Converting 1.25 to 25/100:The whole number part '1' has been ignored. This conversion only accounts for the decimal part. 1.25 = 1 and 25/100, which simplifies to 1 1/4.
FAQ

Questions students ask

What is a recurring decimal?
A recurring decimal (also known as a repeating decimal) is a decimal number that has a digit or a block of digits that repeats infinitely after the decimal point. For example, 0.333... (where the 3 repeats) or 0.121212... (where the 12 repeats).
How do I convert a recurring decimal to a fraction?
You use an algebraic method. Let 'x' equal the recurring decimal. Multiply 'x' by powers of 10 until the recurring part aligns perfectly. Then, subtract the original equation from the multiplied equation to eliminate the recurring part, leaving you with a simple equation to solve for 'x' as a fraction. For example, for 0.333..., let x = 0.333... Then 10x = 3.333... Subtracting gives 9x = 3, so x = 3/9 = 1/3.
Why do some fractions produce recurring decimals?
A fraction will produce a recurring decimal if, when it's in its simplest form, the prime factors of its denominator include any prime numbers other than 2 or 5. If the denominator's prime factors are only 2s and/or 5s, it will produce a terminating decimal. For example, 1/3 produces 0.333... because 3 is a prime factor. 1/7 produces 0.142857... because 7 is a prime factor. But 1/4 (denominator 2x2) produces 0.25, and 1/10 (denominator 2x5) produces 0.1.
How do I simplify a fraction?
To simplify a fraction, you need to divide both the numerator (top number) and the denominator (bottom number) by their Greatest Common Divisor (GCD). The GCD is the largest number that divides into both without leaving a remainder. For example, to simplify 25/100, the GCD of 25 and 100 is 25. Dividing both by 25 gives 1/4. If the GCD is 1, the fraction is already in its simplest form.
What is the difference between a proper fraction and a mixed number?
A proper fraction is a fraction where the numerator is smaller than the denominator (e.g., 1/2, 3/4). Its value is always less than 1. A mixed number is a combination of a whole number and a proper fraction (e.g., 1 1/2, 2 3/4). Its value is always greater than 1. An improper fraction (e.g., 3/2, 5/4) has a numerator greater than or equal to its denominator and can be converted into a mixed number.

Related calculators

Fractions

Fraction to Decimal →

Fractions

Simplify Fractions →

Percentages

Percentage Calculator →