Convert decimal to fraction


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.


However ...


... 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.


Isn't this a little complicated?


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 ...


... an easy way to convert decimal to fraction!


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

 

A quick reminder about place value before more examples!


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)


Now consider


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


Two more!


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.


What about fraction to decimal?


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:

Decimal numbers

Fraction to decimal

Fraction to decimal chart

Decimal to percent

Percent to decimal


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