How to Convert a Decimal to a Fraction

How it works

A decimal is a fraction with a power-of-ten denominator written in place-value form. Converting just writes that fraction out and reduces it to lowest terms: 0.36 = 36/100 = 9/25.

Method 1: read it, write it, simplify it

This is the method most teachers start with, and it works for every decimal that ends.

1. Read the decimal using place value. 0.36 is “thirty-six hundredths”.
2. Write what you said as a fraction. Thirty-six hundredths is 36/100.
3. Simplify. Both 36 and 100 are divisible by 4, giving 9/25. Nine and 25 share no common factor, so 9/25 is the answer.

Method 2: multiply to remove the decimal point

Some people find it easier to think of “making the decimal a whole number”. Put the decimal over 1, then multiply the top and bottom by 10 for every digit after the point.

Example: 0.45 = 0.45/1. There are two decimal places, so multiply top and bottom by 100: 45/100. Simplify by 5: 9/20. This is exactly the same calculation as Method 1, written differently, so use whichever makes more sense to you.

Method 3: change a decimal to a fraction you already know

With practice you will recognise common decimals immediately. Learn the halves, quarters, fifths and eighths, and you can change most everyday decimals to fractions in your head:

Bigger values build on these: 0.05 is a tenth of 0.5, so it is 1/20; 0.0125 is a tenth of 0.125, so it is 1/80.

How to change a decimal greater than 1 to a fraction

Split the number at the decimal point. Keep the whole number, convert the decimal part, then put them together. For 3.4: the 0.4 becomes 4/10 = 2/5, so 3.4 = 3 2/5. As an improper fraction that is (3 × 5 + 2)/5 = 17/5. For negative numbers, convert as if the number were positive and put the minus sign in front of the whole answer.

How to convert a repeating decimal to a fraction

For a decimal that repeats forever, use a little algebra. Let x = 0.272727…. Two digits repeat, so multiply by 100: 100x = 27.272727…. Subtract the first equation from the second and the repeating parts cancel: 99x = 27, so x = 27/99 = 3/11.

If some digits come before the repeat, multiply to move them in front of the decimal point first. The repeating decimal to fraction calculator does every case and shows its working.

How to check your answer

Divide the numerator by the denominator. If you get back the decimal you started with, the fraction is right. For example, 9/25: 9 ÷ 25 = 0.36. ✓ Then check the fraction is fully simplified: if the numerator and denominator are both even, or both end in 0 or 5, you can still divide further.

You can also run any decimal through the decimal to fraction calculator to confirm the answer and see the GCD it used.

Practice questions

Try these, then check your answers below. For a full printable set with an answer key, use the decimal to fraction worksheet.

Tips for students and teachers

• Say the decimal aloud using place value (“three hundred seventy-five thousandths”) — it gives the fraction directly.
• Draw it. A 10 × 10 grid makes hundredths visible: shade 36 squares to see 36/100, then group them to see 9/25.
• Connect to money. $0.25 is a quarter of a dollar; $0.10 is a tenth.
• Practise simplifying separately. Most errors happen in the last step, not in writing the fraction.