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Comparing Decimals with Mixed Numbers

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To compare a decimal and a mixed number,

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

 

For example: Let’s compare 4
1 5
and 4.13.
 

First, let's write the mixed number as a decimal.

 

In order to do so, we first write the fractional part of the mixed number,
1 5
, as a decimal.
 

 

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

 

Now, write
2 10
as a decimal.
 
 
2
10
=  0.2

 

So, 4
1
5
=  4.2 .

 

Now, compare 4.2 and 4.13.

 

As the tenth digit of 4.2 is greater than the tenth digit of 4.13,

 

4.2 > 4.13

 

 

So, 4
1
5
 >  4.13 .