NCERT Solution For Class 9 Math Chapter – 1 Exercise – 1.3

Posted onAuthorDev Bhardwaj

NCERT Solutions For Class 9 Math Chapter – 1 Exercise – 1.3

 

Q1.  Write the following in decimal form and say what kind of decimal expansion each has:

  • 36/100

Solution:-

NCERT Solution For Class 9 Maths Ex-1.3-1

 

 

 

 

 

 

= 0.36 (Terminating)

 

 

  • 1/11

Solution:-

NCERT Solution For Class 9 Maths Ex-1.3-2

 

 

 

 

 

 

 

 

= 0.0909 = 0.09 (Non terminating and repeating)

 

  • 33/8

Solution:-

NCERT Solution For Class 9 Maths Ex-1.3-3

 

 

 

 

 

 

 

= 4.125 (Terminating)

 

  • 3/13

Solution:-

NCERT Solution For Class 9 Maths Ex-1.3-4

 

 

 

 

 

= 0.230769 = 0.230769

 

  • 2/11

Solution:-

 

NCERT Solution For Class 9 Maths Ex-1.3-5

 

 

 

 

 

 

= 0.181818181818 = 0.18 (Non terminating and repeating)

 

 

  • 329/400

Solution:-

NCERT Solution For Class 9 Maths Ex-1.3-6

 

 

 

 

 

 

 

= 0.8225 (Terminating)

 

Q2. You know that 1/7 = 0.1428857 Can you predict what the decimal expansions of 2/7 , 3/7 , 4/7 , 5/7 , 6/7 are , without actually doing the the long division ? If so , how ?

Solution:-

 

1/7 = 0.142857

2 x 1/7 = 2 x 0.142857 = 0.285714

3 x 1/7 = 3 x 0.142857 = 0.428571

4 x 1/7 = 4 x 0.142857 = 0.571428

5 x 1/7 = 5 x 0.142857 = 0.714285

6 x 1/7 = 6 x 0.142857 = 0.857142

 

Q3. Express the following in the form p/q where p and q are integer and q 0.

  • 6

Solution:-

 

0.6 = 0.666….

X =  0.666…

10 x = 6.666…

10 x = 6 + x

X = 2/3

 

  • 47

Solution:-

 

0.47 = 0.4777…

= (4/10) + (0.777/10)

X = 0.777…

10 x = 7.777

10x = 7 + x

X = 7/9

(4/10) + (0.777…/10) = (4/10) + (7/90) (x=7/9 and x = 0.777…..0.777…./10 = 7(9 x 10) = (7/90)

= (36/90) + (7/90) = 43/90

 

  • 01

Solution:-

 

0.0001 = 0.001001….

X = 0.001001…

1000x = 1.001001….

1000x = 1 + x

999x = 1

X = 1/999

 

Q4. 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.

Solution:-

 

X = 0.9999 Eq (a)

Multiplying both sides by 10 ,

10x = 9.9999….. Eq (b)

Eq (b) – Eq (a)  we get

(10x = 9.9999) – (x = 0.9999….)

X = 1

 

 

Q5. 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.

Solution:-

 

Dividing 1 by 17:

NCERT Solution For Class 9 Maths Ex-1.3-7

 

 

 

 

 

 

 

 

 

 

 

 

 

1/17 = 0.0588235294117647

 

Q6. Look at several examples of rational numbers in the form of p/q (q≠0)  where p and q are integers with no common factors other than 1 and having terminating decimal representations ( expansion) Can you guess what property q must satisfy ?

Solution:-

 

Q is 2 , 4 , 5, 8, 10 …..

1/2  = 0.    5, denominator q = 21

7/8 = 0.   875 denominator q = 23

4/5 = 0. 8 , denominator q = 51

 

 

Q7. Write three numbers whose decimal expansions are non – terminating non – recurring.

Solution:-

 

√3 = 1.732050807568

√26 = 5.099019513592

√101 = 10.04987562112

 

Q8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution:-

 

5/7 = 0.714285

9/11 = 0.81

 

These different irrational numbers are:

0.7373007300073000073….

0.75075007300075000075…

0.76076007600076000076…

 

Q9. Classify the following numbers as rational or irrational according to their type:

  • √23

Solution:-

 

It is an irrational number.

 

  • √225

Solution:-

 

It is a rational number.

 

  • 3796

Solution:-

 

It is a rational number.

 

  • 478478

Solution:-

 

It is a rational number.

 

  • 101001000100001…

Solution:-

 

It is an irrational number.