Class 9 Maths Exercise 1.3 | Number System | NCERT Simple Solutions

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Overview

There are 9 questions in Class 9 Maths Exercise 1.3. The questions and their solutions with examples are explained in easy language.

Question/Answers

S.No.Question & Answer
Q.1.Write the following in decimal form and say what kind of decimal expansion each has:
(i) 36/100 (ii) 1/11 (iii) 4⅛
(iv) 3/13 (v) 2/11 (vi) 329/400
Ans.(i) 0.36, Terminating
(ii) 0.09…, Non Terminating
(iii) 33/8= 4.125, Terminating
(iv) 0.230769…, Non Terminating
(v) 0.18…, Non Terminating
(vi) 0.8225, Terminating
Class 9 Maths Exercise 1.3 | Question 1 Solutions

Q.2.You know that 1/7 = 0.142857… Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?
(Hint: Study the remainders while finding the value of 1/7 carefully.)
Ans.1/7= 0.142857… so
2/7= 2×1/7= 2x 0.142857…= 0.285714…
3/7= 3×1/7= 3x 0.142857…= 0.428571…
4/7= 4×1/7= 4x 0.142857…= 0.571428…
5/7= 5×1/7= 5x 0.142857…= 0.714285…
6/7= 6×1/7= 6x 0.142857…= 0.857142…
Q.3.Express the following in the form p/q, where p and q are integers and q ≠0.
(i) 0.6… (ii) 0.47… (iii) 0.001…
Ans.(i) 0.6…= 0.666
Let  x = 0.666…
Then,
10x = 6.666…
10x = 6+0.666
10x = 6 + x
9x = 6
x=6/9
x = 2/3 (which is=0.6…)

(ii) 0.47…= 0.477
Let x= 0.477…
Then,
10x=4.777
10x-x= 4.777-0.477
9x=4.3
x=4.3/9
x=43/90 (which is =0.477…)

(iii) Let x= 0.001…
Then,
10x= 0.011
10x-x= 0.011-0.001
9x=0.01
x= 0.01/9
x= 1/900 (which is =0.001…)
Q.4.Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
Ans.Let x= 0.9999…
10x= 9.999
10x-x= 9.999-0.999
9x= 9
x=9/9
x=1
The difference between 1 and 0.999999 is 0.000001, which is negligible.
As a result, we can conclude that 0.999 is too close to 1, and 1 as the answer is justified.
Q.5.What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.
Ans.The repeating block of the decimal expansion of 1/17 has 16 digits. The image shows the complete answer.

Q.6.Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Ans.When q is 2, 4, 5, 8, 10… The decimal expansion is then completed.
As an example,
1/2=0.5, denominator q = 2¹
7/8 = 0. 875, denominator q = 2³
4/5=0.8, Denominator q = 5¹
We can see that the terminating decimal can be obtained when the prime factorization of the given fractions denominators has the power of only 2 or 5 or both.
Q.7. Write three numbers whose decimal expansions are non-terminating non-recurring.
Ans.Non-terminating non-recurring decimal is a number with an infinite number of digits after the decimal point and no pattern of digit repetition.
Irrational numbers are non-terminating non-recurring decimals.
Examples:
√2 = 1.414213562 ………..
√3 = 1.732050808 …….
√5 = 2.23606797 …….
Q.8.Find three different irrational numbers between the rational numbers 5/7 and 9/11 .
Ans.Let’s use the long division method to find the decimal expansion of 5/7 and 9/11.


We can write 3 irrational numbers between 5/7 and 9/11 as:
(i) 0.721722172221 . . . 
(ii) 0.750975009750009 . . . 
(iii) 0.808008000 . . . 
Q.9.Classify the following numbers as rational or irrational:
(i) √23 (ii) √225 (iii) 0.3796
(iv) 7.478478 (v) 1.101001000100001…
Ans.(i) √23 = √23/1 = p/q but here p is not an integer
so √23 is an irrational number.

(ii) √225 = 15/1, where p and q are integers and q≠ 0
so √225 is a rational number.

(iii) 0.3796
Because 0.3796 is a terminating decimal number, it is a rational number.

(iv) 7.478478 is a rational number because it is a non-terminating recurring decimal, i.e. the number block 478 repeats.

(v) 1.101001000100001…
Because it is a non-terminating and non-recurring decimal, it is an irrational number.

Video Explanation

Maths Concepts

To understand maths concepts of Rational numbers, Integers, etc used in NCERT Class 9 Maths Exercise 1.3, please also check the following articles:

  1. What are Rational and Irrational Numbers
  2. What are Natural Numbers
  3. What are Integers
  4. What are Whole Numbers

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