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Comparing Decimals and Fractions

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To compare a decimal and a fraction,

first convert, or change, one of the numbers so that we have either two decimals or two fractions. Then, compare as usual.

 

For example: Let’s compare
1 2
and 0.72.
 

First, let's write the fraction as a decimal.

 

Write
1 2
as an equivalent fraction with 10 as the denominator.
 
1
2
=
1 × 5
2 × 5
=
5
10

 

Now, write
5 10
as a decimal.
 
 
5
10
=  0.5

 

So,
1
2
=
5
10
=  0.5 .

 

Now, compare 0.5 and 0.72.

 

As the tenth digit of 0.5 is less than the tenth digit of 0.72,

 

0.5 < 0.72

 

 

So,
1
2
<  0.72 .