Q1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?
Ans: We know that a number is said to be rational if it can be written in the form p/q , where p and q are integers and q
Taking the case of '0',
Yes, zero is a rational number.
0 =
Example :
Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.
Hence, 0 is a rational number.
Q2. Find six rational numbers between 3 and 4.
Ans: We can find any number of rational numbers between two rational numbers. There are infinite rational numbers between 3 and 4.
As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)
We can choose 6 rational numbers as: and
Q3. Find five rational numbers between 3/4 and 4/5.
Ans: There are infinite rational numbers between 3/5 and 4/5.
Since we make the denominator same first, then
To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5
with 5+1=6 (or any number greater than 5)
∴ Five rational numbers between areand
Q4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
Ans: True
Natural Numbers: Natural numbers are set of numbers that contain numbers from 1 to infinity. Set of natural numbers is represented as N= {1, 2, 3…….}.
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
Set of Whole numbers is represnted as W= 0,1,2,3….
As all the natural numbers comes in the set of whole numbers. Hence, every natural number is a whole number.
(ii) Every integer is a whole number.
Ans: False
Integers: Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.
i.e., integers = {…4,3,2,1,0,1,2,3,4…}
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers = 0,1,2,3….
Hence, we can say that integers include whole numbers as well as negative numbers.
Every whole number is an integer; however, every integer is not a whole number.
(iii) Every rational number is a whole number.
Ans: False
Rational numbers: All numbers in the form p/q, where p and q are integers and q ≠ 0.
i.e., Rational numbers = 0, 19/30 , 2, 9/3, 12/7…
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers = 0,1,2,3….
Hence, we can say that integers include whole numbers as well as negative numbers.
Every whole number is rational, however, every rational number is not a whole number.
44 videos412 docs55 tests

1. What is the Number System? 
2. What are Natural Numbers? 
3. What is the difference between Whole Numbers and Integers? 
4. How do we classify numbers as Rational or Irrational? 
5. Why are Number Systems important in mathematics? 

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