NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 are part of the NCERT Solutions for Class 9 Maths. Here we have given the NCERT Solutions for Class 9 Maths Chapter 1 Number System Ex 1.1.
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1
Exercise 1.1 Page: 5
Ex 1.1 Class 9 Maths Question 1.
Is zero a rational number? Can you write it in the form pq,where p and q are integers and q ≠0?
Solution:
Yes, zero is a rational number which can be written in the form pq where p and q are integers and q ≠0.
0/1 = 0 ,0/2 = 0, 0/3=0 etc. The denominator q can also be taken as a negative integer.
Taking the case of ‘0’,
We may infer that 0 can be represented in the form p/q, where q may be either a positive or a negative number, because it meets the necessary requirement.
Hence 0 is a rational number.
Also See:
Ex 1.1 Class 9 Maths Question 2.
Find six rational numbers between 3 and 4.
Solution:
Let’s say that qi is a rational number between 3
and 4, where j = 1 to 6. Or you can say that there are infinite number of rational numbers between 3 and 4.
The following are the six rational numbers:
Multiplying both 3 and 4 by 6+1 = 7 will help us find 6 rational numbers between 3 and 4. (or any number greater than 6).
That is, 3 × (7/7) = 21/7
And, 4 × (7/7) = 28/7. The numbers between 21/7 and 28/7 will be rational and between 3 and 4.
Between 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 3 and 4, there are six rational numbers.
Ex 1.1 Class 9 Maths Question 3.
Find five rational numbers between 3/5 and 4/5.
Solution:
There are infinite number of rational numbers between 3/5 and 4/5.
We multiply both 3/5 and 4/5 by 5 to discover 5 rational values between 3/5 and 4/5.
with 5+1=6 (or any number greater than 5)
Since we need to find five rational numbers, multiply the numerator and denominator by 6.
That is, (3/5) × (6/6) = 18/30
And, (4/5) × (6/6) = 24/30
Numbers between 18/30 and 24/30 will be rational and between 3/5 and 4/5.
Therefore, the five rational numbers 19/30, 20/30, 21/30, 22/30, and 23/30 are between 3/5 and 4/5.
Ex 1.1 Class 9 Maths 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
The collection of all natural numbers and 0’s are called whole numbers.
(ii) False
Negative integers are not whole numbers.
(iii) False
Rational numbers p/q are of the form q 0 and q does not exactly divide p which are not whole numbers.
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