EXERCISE 1.1
1.
Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0 %
2. Find six rational numbers between 3 and 4.
3. Find five rational numbers between 3/5 and 4/5
4. State whether the following statements are true or false. Give reasons for your answers.
(1) Every natural number is a whole number.
(11) Every integer is a whole number.
(iii) Every rational number is a whole number.
Answers
0 is a rational number but if Q is equal to zero then it will not be called as the rational number its answer of first part
Answer:
1. Is zero a rational number? Can you write it in the form where p and q are integers and q ≠ 0?
Ans. Yes, zero is a rational number. We can write it in the form
2. Find six rational numbers between 3 and 4.
Ans. We know that there are an infinite number of rational numbers between two rational numbers.
Therefore, six rational numbers between 3 and 4 can be:
Let x = 3 and y = 4, also n = 6
(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d) and (x + 6d).
⇒ The six rational numbers between 3 and 4 are:
3. Find five rational numbers between
⇒ The Five rational numbers between ‘x’ and ‘y’ are:
(x + d); (x + 2d); (x + 3d); (x + 4d)
and (x + 5d).
4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number (iii) Every rational number is a whole number.
Ans. (i) True statement
[ ⇒ The collection of all natural numbers and 0 is called whole numbers]
(ii) False statement
[ ⇒ Integers such as –1, –2 are non-whole numbers]
(iii) False statement
[ ⇒ Rational number is not a whole number]
Exercise– 1.2
1. State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form where m is a natural number.
(iii) Every real number is an irrational number.
Ans. (i) True statement, because all rational numbers and all irrational numbers form the group (collection) of real numbers.
(ii) False statement, because no negative number can be the square root of any natural number.
(iii) False statement, because rational numbers are also a part of real numbers.