Convert terminating and repeating decimals to simplified fractions
Converting decimals to fractions is a key skill in the UK maths curriculum, tested extensively at GCSE level and practised throughout Key Stage 3 and Key Stage 4. Whether you are converting a simple terminating decimal like 0.5 or tackling a repeating decimal like 0.333..., understanding how to express decimals as fractions is fundamental to number fluency. Our decimal to fraction calculator handles both terminating and repeating decimals, automatically simplifying the result to its lowest terms. It shows the fraction, mixed number (where applicable), percentage equivalent, and the full working so you can understand the method behind the conversion. This tool supports the AQA, Edexcel, and OCR GCSE maths specifications, where converting between fractions, decimals, and percentages is a frequently examined topic. Students preparing for exams, teachers creating worked examples, and anyone needing quick fraction conversions will find this calculator invaluable.
To convert a decimal to a fraction: 1. Enter your decimal number in the "Decimal Number" field. This can be positive or negative, and can be greater than 1 (e.g. 1.25). 2. If your decimal is repeating (like 0.333...), toggle "Repeating Decimal?" to Yes and enter the number of digits that repeat. For 0.333..., the repeating digit count is 1 (just the "3" repeats). For 0.142857142857..., it would be 6. 3. For terminating decimals (like 0.75), leave the repeating toggle set to No. 4. Review the results, which show the simplified fraction, mixed number form (if the value is greater than 1), the numerator and denominator separately, and the percentage equivalent. 5. Use the formula display to understand the working. For terminating decimals, it shows how the decimal was placed over a power of 10 and simplified. For repeating decimals, it shows the algebraic method.
For terminating decimals, the conversion method counts the decimal places and creates a fraction over the corresponding power of 10. For example, 0.75 has two decimal places, so it becomes 75/100. Simplifying by the greatest common divisor (GCD of 75 and 100 is 25) gives 3/4. For repeating decimals, the algebraic method is used. Take 0.333... as an example: Let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract the original: 10x - x = 3.333... - 0.333... This gives: 9x = 3 Therefore: x = 3/9 = 1/3 For decimals with both non-repeating and repeating parts (like 0.1666..., where 6 repeats), the method extends by multiplying by appropriate powers of 10 to isolate the repeating portion. When the result is an improper fraction (numerator larger than denominator), the calculator also displays the mixed number form. For example, 5/4 is shown as "1 1/4", separating the whole number from the fractional part. This conversion is central to the National Curriculum for maths. GCSE exam questions frequently ask students to convert recurring decimals to fractions using algebra, and understanding terminating versus repeating decimals connects to whether the denominator's prime factors are limited to 2 and 5.