*Before learning more about how to convert decimal to fraction, please read the primer on decimal numbers and the primer on fractions.*

In the introduction to decimals, it was shown that

**0.1 = 1/10**

i.e. 0.1 equals the proper fraction (numerator less than denominator) 1/10.

Also

**1.2 = 1 + 2/10**

**1.2 = 1 2/10**

i.e. 1.2 is equal to the mixed fraction (whole number + fraction) 1 2/10.

And

**156.6 = 156 + 6/10**

**156.6 = 156 6/10**

i.e. 156.6 equals the mixed fraction 156 6/10.

*These are straightforward conversions of decimals to fractions.*

... it was also shown that

**2.13 = 2 + 1/10 + 3/100**

*While
this provides a neat breakdown, the decimal 2.13 can be expressed as a whole number plus a single fraction.*

Start by adding fractions 1/10 and 3/100.

Find the **least common denominator**, the lowest number into which the denominators 10 and 100 will both divide exactly - the answer's 100.

Leave 3/100 alone - its denominator's already 100. Convert 1/10 into an equivalent fraction containing denominator 100 by multiplying numerator and denominator by factor 10

Now you can write

**2.13 = 2 + 10/100 + 3/100**

*Leaving the denominators alone and adding the numerators*

**2.13 = 2 + 13/100**

2.13 = 2 13/100

i.e. 2.13 is equal to the mixed fraction 2 13/100.

Yes! You probably wouldn't have time in an exam to break down a decimal into a whole number plus tenths (1/10s), hundredths (1/100s) and/or thousandths (1/1000s), then convert to a whole number plus single fraction!

However, you may have already noticed ...

Just write down the

**whole number*** (2 in the case of 2.13)*

followed by a

**single fraction**

- the numerator comprises the digits to the right of the
decimal point *(13 in 2.13's case)*

- the denominator depends on the
least place value - the position occupied by the last digit in the decimal *(in the case of 2.13, the last digit 3 occupies the hundredths [1/100s] position, so the denominator's 100)*

So

**2.13 = 2 13/100**

To the right of the decimal point the

- first digit position represents tenths (1/10s) (denominator 10)
- second digit position hundredths (1/100s) (denominator 100)
- third digit position thousandths (1/1000s) (denominator 1000)

i.e. the decimal 13.089 equals the mixed fraction 13 89/1000.

**0.991 = 991/1000**

The whole number's zero, meaning you only need write down a single fraction - the numerator comprises the digits to the right of the decimal point 991, the last digit 1 occupies the thousandths (1/1000s) position, so the denominator's 1000. The decimal 0.991 is equal to the proper fraction 991/1000.

**2236.47 = 2236 47/100**

Write down the whole number 2236, the numerator of the fraction consists of the digits to the right of the decimal point 47, the last digit 7 occupies the hundredths (1/100s) position, making the denominator 100. The decimal 2236.47 equals the mixed fraction 2236 47/1000.

*Remember you can also go on to convert any mixed fraction to an improper fraction - for example, 1.2 = 1 2/10 = 1 + 2/10 = 10/10 + 2/10 = 12/10 = 6/5. To learn how to do this click here.*

Once you've grasped how to convert decimal to fraction, you may wish to learn how to do the reverse - convert fraction to decimal and create your own fraction to decimal conversion chart!

For more on decimals click: