Question

which of the following rational number will have a terminating decimal expansion. (a)17/8 (b)7/105 (c)9/14 (d)13/30​

Answer 1

Answer:

Correct option is

C

1600

15

If numerator and denominator are co-prime then fraction will terminate only if denominator will be of type 2

m

5

n

.

Now let see the denominator of each option one by one

A. 441 cannot be expressed in the form of 2

m

5

n

.

B. 210 = 7x3x2x5 ;cannot be expressed in the form of 2

m

5

n

C. 1600= . 2

6

5

2

D. Cannot be expressed in the form of 2

m

5

n

.

So the correct answer will option C

Answer 2

Given :  rational numbers

To Find :  which of the following rational number will have a terminating decimal expansion

(a)17/8 (b)7/105 (c)9/14 (d)13/30​

Solution:

Rational number have terminating decimal expansion

if after writing in standard form

Denominator has only factor of form

2ᵃ5ᵇ  where a , b are non negative integers

17/8

= 17/2³

2ᵃ5ᵇ   a = 3 , b = 0

Hence Terminating Decimal

7/105

= 1/15

= 1/(3 * 5)

has 3 also a factor hence non terminating decimal expansion

9/14

= 9/(2 * 7)

has  7 also a factor hence non terminating decimal expansion

13/30

= 13/(2 * 3 * 5)

has 3 also a factor hence non terminating decimal expansion

so  17/8  is   rational number having a terminating decimal expansion.

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