COMPARE TO FRACTIONS AND DECIMALS

Compare Percents to Fractions and Decimals :

In this section, we will learn, how to compare percents to fractions and decimals. 

Compare Percents to Fractions - Steps

Step 1 :

Write the given percentage as fraction.

For example, if it is 15% then write it as 15/100.

Step 2 :

Convert the denominator of the given fraction as 100 using multiplication. 

So that, on either sides we will have fractions with same denominators.

Step 3 :

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

Note : 

If it is not possible to convert the denominator of the given fraction into 100 using multiplication, better convert both percent and fraction into decimal and compare. 

Compare Percents to Decimals - Steps

Step 1 :

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

Step 2 :

Multiply and divide the given decimal by 100.

So that, on either sides we will have fractions with same denominators.

Step 3 :

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

Compare Percents to Fractions and Decimals - Examples

Example 1 :

Which of the following signs makes the statement true ?

< ,  > ,  =

Solution :

We can write 20% as shown below. 

20 / 100 -----(1)

Multiply both numerator and denominator of the fraction 1/2 by 50 as shown below.

(1 / 2) ⋅ (50 / 50)  =  50 / 100 -----(2)

In fractions (1) and (2), the denominators are same.

Now, we can compare the numerators.

20 is lesser than 50

So, 20% is lesser than 1/2.

Example 2 :

Which sign makes the statement true?

< ,  > ,  =

Solution :

Here, both the quantities are percents.

So, we can easily compare them. 

65% is greater than 62%

Example 3 :

Which sign makes the statement true?

< ,  > ,  =

Solution :

We can write 7% as shown below. 

7 / 100 -----(1)

Multiply both numerator and the denominator of the fraction 1/4 by 25 as shown below.

(1 / 4) ⋅ (25 / 25)  =  25 / 100 -----(2)

In fractions (1) and (2), the denominators are same.

Now, we can compare the numerators.

7 is lesser than 25 

So, 7% is lesser than 1/4.

Example 4 :

Which sign makes the statement true?

< ,  > ,  =

Solution :

In the fraction 79/100, already the denominator is 100.

So, we have nothing more to do in the fraction 79/100.

79 / 100 -----(1)

We can write 79% as shown below. 

79 / 100 -----(2)

In fractions (1) and (2), both the numerators and denominators are same.

So, 79/100 and 79% are equal.

Example 5 :

Which sign makes the statement true?

< ,  > ,  =

Solution :

We can write 3% as shown below. 

3 / 100 -----(1)

Multiply and divide the decimal 0.07 by 100 as shown below. 

0.07 ⋅ (100 / 100)  =  7 / 100 -----(2)

In fractions (1) and (2), the denominators are same.

Now, we can compare the numerators.

3 is lesser than 7

So, 3% is lesser than 0.07

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

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