SETS OF REAL NUMBERS WORKSHEET

Question 1 : 

Classify the number given below by naming the set or sets to which it belongs.

37

Question 2 : 

Classify the number given below by naming the set or sets to which it belongs.

-98

Question 3 : 

Classify the number given below by naming the set or sets to which it belongs.

√5

Question 4 : 

Classify the number given below by naming the set or sets to which it belongs.

-56.12

Question 5 : 

Classify the number given below by naming the set or sets to which it belongs.

2√3

Question 6 : 

Classify the number given below by naming the set or sets to which it belongs.

7/8

Question 7 : 

Classify the number given below by naming the set or sets to which it belongs.

102.353535......

Question 8 : 

Classify the number given below by naming the set or sets to which it belongs.

√25

Detailed Answer Key

Question 1 : 

Classify the number given below by naming the set or sets to which it belongs.

37

Answer : 

Whole, Integer, Rational

37 is a whole number.

All whole numbers are integers. All integers are rational numbers.

Question 2 : 

Classify the number given below by naming the set or sets to which it belongs.

-98

Answer : 

Integer, Rational

-98 is an integer.

All integers are rational numbers.

Question 3 : 

Classify the number given below by naming the set or sets to which it belongs.

√5

Answer : 

Irrational

5 is in square root. It is a whole number, but it is not a perfect square. 

So, √5 is irrational.

Question 4 : 

Classify the number given below by naming the set or sets to which it belongs.

-56.12

Answer : 

Rational

-56.12 is a rational number.

It is not a whole number because it is negative. It is not an integer because there are non-zero digits after the decimal point.

Question 5 : 

Classify the number given below by naming the set or sets to which it belongs.

2√3

Answer : 

Irrational

We have 3 in square root. 3 is a whole number, but it is not a perfect square. 

So, √3 is irrational. 

We already know the fact, if an irrational number is multiplied by a rational number, the product is irrational. 

So, 2√3 is irrational.

Question 6 : 

Classify the number given below by naming the set or sets to which it belongs.

7/8

Answer : 

Rational

7/8 is a rational number.

It is not a whole number, because it is a fraction of a whole number. It is not an integer because it is not a whole number or the opposite of a whole number.

Question 7 : 

Classify the number given below by naming the set or sets to which it belongs.

102.353535......

Answer : 

Rational

102.353535........is a rational number.

Since 102.353535...... is a recurring decimal, it can be converted into fraction. And also it is not a whole number or integer, because it is a fraction. 

Question 8 : 

Classify the number given below by naming the set or sets to which it belongs.

√25

Answer : 

Whole, Integer, Rational

25 is in square root. 25 is a whole number and also it is a perfect square. 

So, we have

√25  =  √(5x5)  =  5

So, √25 is whole, integer, rational

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