Decimal number:
Trailing decimal places to repeat (optional):

Results will appear here

Fraction Result

Use this calculator to convert a decimal number to a fraction. To convert a number with repeating decimals, enter the number of trailing decimal places (digits from the end of the number) to repeat.

Disclaimer: Whilst every effort has been made in building our calculator tools, we are not to be held liable for any damages or monetary losses arising out of or in connection with their use. Full disclaimer.

How to convert a decimal to a fraction

To convert a decimal to a fraction, take the decimal number and write it as the numerator (top number) over its position value. As an example, for 0.4 you'd find the four is in the tenths position. To turn it into a fraction, place the 4 over 10, to give 4/10. You can then simplify the fraction if needed. In this example, we can simplify to 2/5.

Some decimals are so familiar to us that we can instantly see them as fractions: if your sister is 14.5 years old, you know that she's 14 1/2. If you buy a bag of potatoes weighing 0.75kg, you know that it's 3/4 of a kilo. If you give your sister a 1/3 kilo bag of potatoes for her 18th birthday, you know that your chances of a polite and enthusiastic response are around 0.1, or 1/10.

But what of other less obvious decimals — how can you calculate what 0.45, 0.62 or 0.384 as a fraction, for example? Here's how...

Converting a decimal to a fraction – step by step

The most important thing you need to keep in mind when you want to convert a decimal to a fraction is that a decimal expresses whether something is a 'tenth', a 'hundredth', a 'thousandth' etc., based on its position after the decimal point. If you're looking at a decimal which only has one number after the point, then you are working in tens. If your decimal has two digits after the point, then you will be working in hundreds. If your decimal has three digits after the point, then you are working in thousands, and so on.

1

Establish whether your decimal is working in tens, hundreds, thousands or more. This will become your multiplier in step 3.

Example: 0.45 is 45 hundredths
2

Write the decimal number as the numerator (top number) of a fraction over the multiplier.

Example: 45/100
3

Multiply both the numerator and the denominator by the same number until you arrive at the same value (the GCD, or greatest common divisor).

Example: GCD of 45 and 100 is 5
4

Simplify (reduce) the fraction by dividing both the numerator and denominator by the GCD.

Example: 45 ÷ 5 = 9, 100 ÷ 5 = 20 → 9/20
5

Review your fraction — if both the numerator and denominator can still be divided evenly, keep reducing.

Example: 9/20 cannot be reduced further ✓

Should you have a decimal number greater than 1 (such as 1.6), you would first separate out your decimal number, convert to a fraction, and then add the whole number back in.

If you manage to arrive at a fraction where neither the numerator nor denominator can be divided evenly, it's not your imagination — you've arrived at an irreducible fraction, also known as a fraction in its lowest terms. This is also known as an irrational number. 🎉

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Using the decimal to fraction calculator

You can use our decimal to fraction calculator to check your calculation answers or to get help with figuring out the methodology behind converting a decimal number to a fraction. As well as providing a result for your calculation, we also show you how the answer was achieved.

Repeating decimals

Our calculator gives you the opportunity to represent repeating decimals by entering a figure into the 'Number of trailing decimal places to repeat' box. Simply enter the number of digits from the end of the decimal to repeat. For other non-repeating decimals, keep the default setting at 0.

As an example, if you want to convert a repeating decimal such as 1.234... then you should enter 1.234 into the Decimal number box and 3 into the Trailing decimal places to repeat box (signifying that the last 3 digits of the number should repeat).