PERCENTS GREATER THAN 100 AND LESS THAN 1

In a fraction, when the numerator is smaller than the denominator, the percent is either between 1% and 100 % or less than 1 %.  

To make sure that the given fraction is less than 1%, better convert the given fraction into decimal and then convert into percent.  

In decimal, when the given value is greater than 1, the percent is greater than 100%.    

In decimal, when the given value is less than 1, the percent is either between 1% and 100% or less than      1%.      

To make sure that the given decimal is less than 1%, better convert the given decimal into percent.   

All mixed numbers/fractions are greater than 100%

Example 1 :

Classify the fraction 17 / 5 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

In the fraction 17 / 5, the numerator is greater than denominator.

So the fraction 17 / 5 is greater than 100%.

More clearly, 

In the above calculation, the fraction 17 / 5 is equal to 340% which is greater than 100%.  

Example 2 :

Classify the fraction 7 / 25 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

In the fraction 7 / 25, the numerator is less than denominator.

From the above point, all we can conclude is, the fraction 7 / 25 is not greater than 100%. 

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given fraction into percent as given below. 

In the above calculation, the fraction 7 / 25 is equal to 28% which is between 1% and 100%. 

Example 3 :

Classify the fraction 3 / 8 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

In the fraction 3 / 8, the numerator is less than denominator.

From the above point, all we can conclude is, the fraction 3 / 8 is not greater than 100%. 

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given fraction into percent as given below. 

In the above calculation, the fraction 3 / 8 is equal to 37.5% which is between 1% and 100%. 

Example 4 :

Classify the fraction 13 / 8 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

In the fraction 13 / 8, the numerator is greater than denominator.

So the fraction 13 / 8 is greater than 100%.

More clearly,

In the above calculation, the fraction 13 / 8 is equal to 162.5% which is between 1% and 100%. 

Example 5 :

Classify the fraction 3 / 800 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

In the fraction 3 / 800, the numerator is less than denominator.

From the above point, all we can conclude is, the fraction 3 / 800 is greater than 100%. 

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given fraction into percent as given below. 

In the above calculation, the fraction 3 / 800 is equal to 0.375% which is less than 100%. 

Example 6 :

Classify the decimal  2.742 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

The value of the given decimal is greater than 1.

So, it is greater than 100%

More clearly, 

In the above calculation, the decimal 2.742 is equal to 274.2% which is greater than 100%. 

Example 7 :

Classify the decimal  0.2742 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

The value of the given decimal is less than 1.

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given decimal into percent as given below. 

In the above calculation, the decimal 0.2742  is equal to 27.42% which is between 1% and 100%. 

Example 8 : 

Classify the decimal  0.0032 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

The value of the given decimal is less than 1.

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given decimal into percent as given below. 

In the above calculation, the decimal 0.0032 is equal to 0.32% which is less than 1%.

Example 9 :

Classify the decimal  0.032 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

The value of the given decimal is less than 1.

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given decimal into percent as given below. 

In the above calculation, the decimal 0.0.032  is equal to 3.2% which is between 1% and 100%. 

Example 10 :

Classify the decimal  0.32 as

(A) less than 1 %

(B) greater than 100%

(C) between 1% and 100%

Solution : 

The value of the given decimal is less than 1.

It may be either between 1% and 100% or less than 1%. 

To make sure of the category, let us convert the given decimal into percent as given below. 

In the above calculation, the decimal 0.0.32  is equal to 32% which is between 1% and 100%. 

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.