Decimal to Fraction Calculator
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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'll 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 3/4 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 is 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.
- 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
- Write out your decimal as the numerator of a fraction (i.e. above the fraction line). The denominator below the line is always 1, because a decimal is always part of 1.
- Multiply your numerator by 10 / 100 / 1000 (your multiplier from step 1), and then do the same for the denominator.
- Simplify your fraction. Find the 'Greatest Common Factor' (the highest number that divides exactly into both the numerator and the denominator).
Example: Both 45 and 100 are multiples of 5, so we can divide both numbers by 5. Result: 9/20.
Should you have a whole number at the beginning of your decimal (6.45), you can simply remove it to work out your decimal, then include it again at the end (Example: 6 and 9/20).
If you manage to find a number which simply can't become a fraction, then don't be too hard on yourself. It's not you: it's them. These are called "irrational numbers", and with good reason. One example of an irrational number is pi (3.14159265...) There's just no reasoning with them.
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.
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).
Other math and education calculators
The Calculator Site features a number of popular math and education calculators. You may, for example, wish to add, subtract, multiply, divide or simplify fractions. Alternatively, you may be at university and need to calculate your weighted grade.
And, if you find yoursefl needing some assistance with rounding calculations to significant figures, check out the Significant Figures Calculator by Quentin Truong.