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How to Convert Fractions to Decimals


Some examples of where we want to try and convert fractions to decimals can sometimes be a bit tougher than when trying to do the opposite and change a decimal number to a fraction.

Here on this page, we look to show clearly how to convert fractions to decimals when required.

Converting some standard fractions to decimal form can be simpler than others,

such as the fraction   \bf{\frac{1}{4}}.




Convert Fractions to Decimals,
an Effective Method:


A suitable approach to change a fraction like  \bf{\frac{1}{4}}  to a decimal is to firstly focus on the denominator on the bottom.

Where we then try to establish another number that the denominator can be multiplied with,
so that the result is a power of  10,  such as  10,  100,  1000  etc.

For   \bf{\frac{1}{4}}   ,   4 × 25 = 100.

So:     \boldsymbol{\frac{1 \space \times \space 25}{4 \space \times \space 25}}   =   \bf{\frac{25}{100}}

( Multiplication of top AND bottom keeps overall fraction value the same )


Cases of dividing a number by  10,  100  etc,
can be viewed at the  division of decimals  page.

\bf{\frac{25}{100}}   =   0.25

So the decimal form of the fraction  \bf{\frac{1}{4}}  is  0.25.




Examples    


(1.1) 

Convert the fraction   \bf{\frac{72}{100}}   to decimal form.

Solution   

A simple example such as this one can be done very quickly.

\bf{\frac{72}{100}}   =   0.72




(1.2) 

Convert the fraction   \bf{\frac{5}{8}}   to a decimal.

Solution   

8 × 125  =  1000

=>   \boldsymbol{\frac{5 \space \times \space 125}{8 \space \times \space 125}}   =   \bf{\frac{625}{1000}}   =   0.625




(1.3) 

Convert the fraction   3\bf{\frac{2}{5}}   to decimal form.

Solution   

The first thing to do to with a change fractions to decimals example such as this one, is to leave the whole number to one side, and concentrate just on the fraction.

5 × 2  =  10

=>   \boldsymbol{\frac{2 \space \times \space 2}{5 \space \times \space 2}}   =   \bf{\frac{4}{10}}   =   0.4

Now bringing the whole number back, and placing it in front of the decimal point, to form the complete decimal number.

3\bf{\frac{2}{5}}   =   3.4







How to Convert Fractions to Decimals,
Further


An alternative approach that can be used when attempting to change fractions to decimals is to treat the fraction as a division sum.



Examples    


(2.1) 

Convert   \bf{\frac{3}{8}}   to a decimal.

Solution   

1)
Firstly set up as a standard division sum.

8 3        


Then place a decimal point after the 3, and also above at the same place.
      .
8 3.    


2)
Now we want to place some zeroes after the decimal point below, depending how many decimal places we want wish to have in the decimal form.
We will try 4 zeroes here and see how things turn out.

      .
8 3.0000


3)
Now we treat this as if it was the division sum  3000 ÷ 8.

   0.3 7 5 0
8 3.06040 0

At this point it becomes clear that no matter how many zeroes we had used, every division here after the 3rd decimal place just give 0.

This is because the fraction  \bf{\frac{3}{8}}  converts to a terminating decimal, with only 3 digits after the decimal point.

So   \bf{\frac{3}{8}}  =  0.375   in decimal form.




(2.2) 

Convert the fraction   \bf{\frac{3}{7}}   to a decimal with 3 decimal places.

Solution   

This is a fraction that doesn’t terminate like the previous fraction  \bf{\frac{3}{8}}  did.

So it’s specified that we will look to obtain a decimal form of the fraction that is to 3 decimal places.

To do this accurately, we will initially need to place 4 zeroes after the decimal point below in our sum, as the 4th division will tell us whether to round up or down at the 3rd decimal place.

1)
      .
7 3.0000

2)
    0.4 2 8 5
7 3.0206040


Forgetting about remainders, the 4th division resulted in 5, so we round up at the 3rd decimal place to give 0.429.

The fraction   \bf{\frac{3}{7}}  =  0.429   in decimal form to three decimal places.




(2.3) 

Convert the fraction   \bf{\frac{9}{7}}   to a decimal with 4 decimal places.

Solution   

Similar to  \frac{3}{7}.

This time we’ll take the same approach but look to obtain a decimal number to  4  decimal places, assuming the expansion reaches that far.

1)
      .
7 9.0000

2)
    1. 2 8 5 7 1
7 9.2060405010

Again not worrying about remainders, here the 5th division after the decimal resulted in  1,  so we round down at the 4th decimal place to give  1.2857.

The fraction   \bf{\frac{8}{7}}  =  1.2857   in decimal form to four decimal places.





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