# Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.1

Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.1 Textbook Questions and Answers.

## BSEB Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.1 Question 1.
Is zerc a rational number? Can you write it in P the form $$\frac { p }{ q }$$, where p and q are integers and q ≠ 0?
Solution:
Yes,-zero is a rational number.
Zero can be written in any of the following forms :
$$\frac { 0 }{ 1 }$$, $$\frac { 0 }{ -1 }$$, $$\frac { 0 }{ 2 }$$, $$\frac { 0 }{ -2 }$$ and so on.
Thus, 0 can be written as $$\frac { p }{ q }$$, where p = 0 and q is any non-zero integer.
Hence, 0 is a rational number.

Question 2.
Find six rational numbers between 3 and 4.
Solution:
We know that between two rational numbers x and y, such that x < y, there is a rational number $$\frac { x+y }{ 2 }$$. That is, x < $$\frac { x+y }{ 2 }$$ < y
A rational number between $$\frac { 1 }{ 2 }$$ and 4 is $$\frac { 1 }{ 2 }$$(3 + 4) i.e., $$\frac { 7 }{ 2 }$$
∴ 3 < $$\frac { 7 }{ 2 }$$ < 4
Now, a rational number between 3 and $$\frac { 7 }{ 2 }$$ is Hence, six rational numbers between 3 and 4 are :
$$\frac { 25 }{ 8 }$$, $$\frac { 13 }{ 4 }$$, $$\frac { 7 }{ 2 }$$, $$\frac { 15 }{ 4 }$$, $$\frac { 31 }{ 8 }$$ and $$\frac { 63 }{ 16 }$$

Alternative Method
Since we want 6 rational numbers between 3 and 4, so we write 3 = $$\frac{3 \times 7}{1 \times 7}$$ = $$\frac { 21 }{ 7 }$$ and 4 = $$\frac{4 \times 7}{1 \times 7}$$ =
We know that 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28
⇒ $$\frac { 21 }{ 7 }$$ < $$\frac { 22 }{ 7 }$$ < $$\frac { 23 }{ 7 }$$ < $$\frac { 24 }{ 7 }$$ < $$\frac { 25 }{ 7 }$$ < $$\frac { 26 }{ 7 }$$ < $$\frac { 27 }{ 7 }$$ < $$\frac { 28 }{ 7 }$$.
Hence, six rational numbers between 3 = $$\frac { 21 }{ 7 }$$ and 4 = $$\frac { 28 }{ 7 }$$ are $$\frac { 22 }{ 7 }$$, $$\frac { 23 }{ 7 }$$, $$\frac { 24 }{ 7 }$$, $$\frac { 25 }{ 7 }$$, $$\frac { 26 }{ 7 }$$ and $$\frac { 27 }{ 7 }$$. Question 3.
Find five rational numbers between $$\frac { 3 }{ 5 }$$ and $$\frac { 4 }{ 5 }$$.
Solution:
Since we want 5 rational numbers between $$\frac { 3 }{ 5 }$$ and $$\frac { 4 }{ 5 }$$, so we write
$$\frac { 3 }{ 5 }$$ = $$\frac{3 \times 6}{5 \times 6}$$ = $$\frac { 18 }{ 30 }$$
$$\frac { 4 }{ 5 }$$ = $$\frac{4\times 6}{5 \times 6}$$ = $$\frac { 24 }{ 30 }$$
We know that 18 < 19 < 20 < 21 < 22 < 23 < 24
⇒ $$\frac { 18 }{ 30 }$$ < $$\frac { 19 }{ 30 }$$ < $$\frac { 20 }{ 30 }$$ < $$\frac { 21 }{ 30 }$$ < $$\frac { 22 }{ 30 }$$ < $$\frac { 23 }{ 30 }$$ < $$\frac { 24 }{ 30 }$$
Hence, 5 rational numbers between $$\frac { 3 }{ 5 }$$ = $$\frac { 4 }{ 5 }$$ = $$\frac { 24 }{ 30 }$$ are : $$\frac { 19 }{ 30 }$$, $$\frac { 20 }{ 30 }$$, $$\frac { 21 }{ 30 }$$, $$\frac { 22 }{ 30 }$$, $$\frac { 23 }{ 30 }$$ and $$\frac { 24 }{ 30 }$$.

Question 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.
Solution:
(i) True : Every natural number lies in the collection of whole numbers.
(ii) False – 3 is not a whole number.
(iii) False : $$\frac { 3 }{ 5 }$$ is not a whole number.