Exercise 1.4

Question 1. Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion:

(1) 13/3125

Solution: 13/3125 = 13/5⁵

Here, denominator = 5⁵ Which is of the form 2ⁿx5ᵐ(n=0,m=5)

So, the rational number 13/3125 has a terminating decimal expansion.

(2) 17/8

Solution: 17/8 = 17/2³,which is of the

form 2ⁿx5ᵐ

Here,denominator = 2³which of the form 2ⁿx5ᵐ (n=3,m=0)

So, the rational number 17/8 has a terminating decimal expansion.

(3) 64/455

Solution: 64/455 = 64/5x7x13

Here, denominator =5x7x13, which is not in the form 2ⁿx5ᵐ

So, the rational number 64/455 has a non- terminating non repeating decimal expansion .

(4) 15 /1600

Solution : Here, denominator=2⁶x5,which of the form 2ⁿx5ᵐ

So, the rational number 15/1600 has a terminating decimal expansion.

(5) 29/343

Solution: 29/343 = 29/7³

Here, denominator=7³,which is not of the form 2ⁿx5ᵐ

So, the rational number 29/343 has a non terminating repeating decimal expansion.

(6) 23/2³x5²

Solution: Here, denominator = 2³x5², which is of the form 2ⁿx5ᵐ

So, the rational number 23/2³x5² has a terminating decimal expansion.

(7) 129/2²x5⁷x7⁵

Solution : Here,denominator=2²x5⁷x7⁵,which is not of the form 2ⁿx5ᵐ.

So, the rational number 129/2²x5⁷x7⁵ has a non terminating repeating decimal expansion.

(8) 6/15

Solution : 6/15 = 2/5

Here, denominator =5, which is of the form 2ⁿx5ᵐ.

so, the rational number 6/15 has a terminating decimal expansion.

(9) 35/50

Solution : 35/2x5²=7/2x5

Here, denominator = 2x5,which of the form 2ⁿx5ᵐ.

So, the rational number 35/50 Has a terminating decimal expansion.

(10) 77/210

Solution : 77/210 = 11/30 = 11/2x3x5

Here,denominator = 2x3x5,which is not of the form 2ⁿx5ᵐ

So, the rational number 77/210 has a non-terminating repeating decimal expansion.

QUESTION 2. Write down the decimal expansion of those rational number in question 1 above which have terminating decimal expansion.

(i) 13/3125 =0.00416

13/3125=13×32/3125×32=416/100000=0.00416

(ii) 17/8 = 2.125

(iv) 15/1600 = 0.009375

(vi) 23/2³x5² = 23/200 = 0.115

(viii) 6/15 = 0.4

(ix) 35/50 = 0.7

Question 3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form P/q, What can you say about the prime factor of q?

(i) 43.123456789

Solution : 43.123456789 = 43.123456789/10⁹ = 43123456789/2⁹x5⁹

Here, the denominator is of the form 2ⁿx5ᵐ.

Hence, the number is a rational number, specially a terminating decimal.

(ii) 0.120120012000120000.......

Solution : since the given decimal number is non-terminating non-repeating.it is not rational

(iii)43.123456789123456789123456789.........

Solution : since the given decimal number is non-terminating non-repeating.It is rational, but the denominator is not of the form 2ⁿx5ᵐ.

We hope CBSE/MP Board Class 10th Maths Exercise 1.4 will help you.

Written By - Abhishek Dohare