Our easy-to-use calculator converts fractions into decimals or decimals into fractions.

Enter a fraction to see its equivalent decimal form or input a decimal number to convert it to a fraction.

Our easy-to-use calculator converts fractions into decimals or decimals into fractions.

Enter a fraction to see its equivalent decimal form or input a decimal number to convert it to a fraction.

Click any fraction to see it as a decimal:

A fraction represents a part or a portion of a whole thing. This ‘thing’ could be an amount of money, a group of people, or an item of food. For example, if you were to cut a cake into 4 slices and give it to four people, each person would have ¼ of the cake.

Fractions are made up of two parts: the **numerator** and the **denominator**. The number above the horizontal line is called the numerator. It tells us how many parts of the whole there is. The number below the line is called the denominator, and this tells us how many equal parts the whole has been divided into. Using our example above, the numerator would be 1 and the denominator would be 4.

There are seven different types of fractions: proper fraction, improper fractions, mixed fractions, like and unlike fractions, unit fractions and equivalent fractions.

A proper fraction is a fraction where the numerator (number at the top) is less than the denominator (number at the bottom). For example, ^{2}⁄_{8}, ^{3}⁄_{8} and ^{4}⁄_{9} are all proper fractions.

An improper fraction is where the denominator is a larger number than the numerator. For example, ^{7}⁄_{4} and ^{12}⁄_{8} are both improper fractions.

The value of an improper fraction is always greater than or equal to 1.

A mixed fraction is a combination of a whole number and a fraction e.g. 3 ^{1}⁄_{3}

A mixed fraction is always greater than 1 and can always be converted into an improper fraction. For example 3 ⅓ can be written as ^{10}⁄_{3} .

Fractions that have the same denominators are called like fractions e.g. ^{1}⁄_{5}, ^{2}⁄_{5} and ^{3}⁄_{5}.

Fractions that have different denominators are called unlike fractions e.g. ^{2}⁄_{3}, ^{4}⁄_{5} and ^{6}⁄_{8}.

Any fraction where the numerator is 1 is referred to as a unit fraction e.g. ½, ⅓ and ¼.

Equivalent fractions have different numerators and denominators but result in the same value when simplified. For example, ^{2}⁄_{6} and ^{4}⁄_{12} can be converted into their simplest form of ^{1}⁄_{3}.

To calculate equivalent fractions you can either multiply or divide the numerator and denominator by the same number.

A reduced fraction is when a fraction is in its simplest form. This means that it is not possible to reduce the numerator and denominator to a smaller number. For example, the fraction ^{2}⁄_{4} can be simplified by dividing the numerator and denominator by 2 to equal ¼. It is not possible to reduce ¼ any further so this fraction is now in its reduced form.

Decimals are numbers where a whole number and a fractional part is separated by a decimal point e.g. 2.5. In the decimal value system (the order of the numbers after the decimal point) each entry has a value that is ^{1}⁄_{10} smaller than the value to its left.

The first place after the decimal points is called the “tenths” and has a value of ^{1}⁄_{10}, or 0.1 in decimal form. The second place digit is called the “hundreths” and has a value of ^{1}⁄_{100}, or 0.01. The third place is called the “thousandths” and has a value of ^{1}⁄_{1000}, or 0.0001. If there are more decimals numbers then the value system continues with “ten thousandths”, “hundred thousandths” and so on.

The fractional part of any decimal always has a value less than 1.

A terminating decimal, also known as a non-recurring decimal, has a finite number of digits after the decimal point. For example, 12.2 or 45.2356. These numbers could both be represented with repeating zeros (12.20000 and 45.23560000) but when the repeating digit is “0”, it is referred to as a terminating decimal.

If you want to manually convert a terminating decimal to a fraction, then simply follow the steps below:

**Step 1**: Write the decimal number as a fraction with the decimal as the numerator (the top number) and 1 as the denominator (the bottom number).

1.264

1000

**Step 2**: Count how many numbers are to the right of the decimal point and multiply the numerator and denominator by 10 for each digit. For 1.264 we need to multiply by 10^3. Our calculation now becomes:

^{1264}⁄_{1000}

**Step 3**: Find the Greatest Common Factor of the numerator and the denominator and divide both numbers.

GCF = 8

**Step 4**: Reduce the fraction into its simplest form.

**1 ^{33}⁄_{25}**

A non-terminating decimal, also known as a recurring decimal, has an infinite number of digits and continues endlessly e.g. 32.465256896……

When a block of digits in the sequence repeats itself – as long as the repeating digits are not all zero – this is known as a non-terminating, repeating decimal e.g. 2.123123123.

Typically, non-terminating decimals can be more difficult to convert into fractions but it is still easy enough to do if you follow the below steps. We will use 0.33333… as our example

**Step 1**: Identify the non-terminating decimal and replace it with the value x

x = 0.3333…

**Step 2**: If the repeating sequence is the same number then multiply x by 10. If the sequence is two repeating numbers then multiply by 100 (and so on).

0.3333 x 10 = 3.3333…

**Step 3**: Subtract the equation in step 1 by the equation in step 2.

x = 0.3333 – 10x = 3.3333 = 9x = 3

**Step 4**: Write out the fraction and simplify if possible.

x= ^{3}⁄_{9}

x= ^{1}⁄_{3}

**0.3333… = ^{1}⁄_{3}**