COMPARE TO FRACTIONS AND DECIMALS

About "Compare percents to fractions and decimals"

Compare percents to fractions and decimals :

Percent means out of 100. Here we are going to learn how to compare percents to fractions and decimals.

Steps to be followed in comparing percents to fractions :

(i)  Write the given percentage as fraction. That is, if we have 15% then write it as 15/100.

(ii)  Try to convert the denominator of the given fraction as 100. 

(iii)  If it is not possible then convert both fraction and percent as decimal and compare.

Steps to be followed in comparing percents to decimals :

(i)  Write the given percentage as fraction. That is, if we 15% then write it as 15/100.

(ii)  Multiply and divide the given decimal by 100.So that on either sides we will have fractions with same denominators.

(iii) Now we can easily compare the numerators and decide which number is greater and which number is smaller.

Let us look into some example problems based on the above concept.

Example 1 :

Which sign makes the statement true?

  < ,  > ,  =  

Solution :

We can write 20% as 20/100.

20/100  =  0.2

By multiplying the denominator of the given fraction by 50, we can get 100 in the denominator.

(1/2) x (50/50)  =  50/100  =  0.5

By comparing 0.2 and 0.5, 0.5 is greater. 

So, 20% is lesser than 1/2.

Example 2 :

Which sign makes the statement true?

  < ,  > ,  =  

Solution :

65%  =  65/100

62%  =  62/100

Since the denominators are same, we may compare the numerators and decide which fraction is greater.

65 is greater than 62. So, 65% is greater than 62%.

Example 3 :

Which sign makes the statement true?

  < ,  > ,  =  

Solution :

We can write 7% as 7/100.

7/100  =  0.07

By multiplying the denominator of the given fraction by 25, we can get 100.

(1/4) x (25/25)  =  25/100  =  0.25

By comparing 0.07 and 0.25, 0.07 is lesser. 

So, 7% is lesser than 1/4.

Example 4 :

Which sign makes the statement true?

  < ,  > ,  =  

Solution :

We can write 79% as 79/100.

Since the denominators are same, we can compare the numerators.

79  =  79.

So, both fractions are equal.

Example 5 :

Which sign makes the statement true?

  < ,  > ,  =  

Solution :

We can write 3% as 3/100.

By multiplying the given decimal by 100, we can get rid of the decimal point

0.07 x (100/100)  =  7/100

Now, the denominators the, so we shall compare the numerators and decide which is greater.

By comparing 3 and 7, 3 is lesser. 

So, 3% is lesser than 0.07

After having gone through the stuff given above, we hope that the students would have understood "Compare percents to fractions and decimals". 

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