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.