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NCERT Solutions for Class 9 Maths Chapter 1 Number Systems
NCERT Solutions for Class 9 Maths Chapter 1 Number Systems are prepared by CBSE student eCARE expert to score good marks in class 9. This chapter contain many topics which are very important to score good in class 9. There are some important topic/Activity mentioned below-
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 it can be written in the form pq.
0 = 01 = 02 = 03 etc. denominator q can also be taken as negative integer.
(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 is called whole numbers.
(ii) False
? Negative integers are not whole numbers.
(iii) False
? Rational numbers are of the form p/q, q ≠ 0 and q does not divide p completely that are not whole numbers.
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Some questions are asked by class 9 students related to Maths
Question 1.
Write the following in decimal form and say what kind of decimal expansion each has
Solution:
(i) We have, 36100 = 0.36
Thus, the decimal expansion of 36100 is terminating.
(ii) Dividing 1 by 11, we have
Thus, the decimal expansion of 111 is non-terminating repeating.
(iii) We have, 418 = 338
Dividing 33 by 8, we get
∴ 418 = 4.125. Thus, the decimal expansion of 418 is terminating.
(iv) Dividing 3 by 13, we get
Here, the repeating block of digits is 230769
∴ 313 = 0.23076923… = 0.230769¯
Thus, the decimal expansion of 313 is non-terminating repeating.
(v) Dividing 2 by 11, we get
Here, the repeating block of digits is 18.
∴ 211 = 0.1818… = 0.18¯
Thus, the decimal expansion of 211 is non-terminating repeating.
(vi) Dividing 329 by 400, we get
∴ 329400 = 0.8225. Thus, the decimal expansion of 329400 is terminating.
Ex 1.3 Class 9 Maths Question 2.
You know that 17 = 0.142857¯. Can you predict what the decimal expansions of 27 , 137 , 47 , 57 , 67 are , without actually doing the long division? If so, how?
Solution:
We are given that 17 = 0.142857¯.
∴ 27 = 2 x 17 = 2 x (0.142857¯) =0.285714¯
37 = 3 x 17 = 3 x (0.142857¯) = 0.428571¯
47 = 4 x 17 = 4 x (0.142857¯) = 0.571428¯
57 = 5 x 17 = 5 x(0.142857¯) = 0.714285¯
67 = 6 x 17 = 6 x (0.142857¯) = 0.857142¯
Thus, without actually doing the long division we can predict the decimal expansions of the given rational numbers.