Question

Which of the following has a terminating decimal expansion?
(a) 23/200
(b) 17/9
(c) 8/75
(d) 3/35

Answer 1

Answer:

(c) 8/75

Step-by-step explanation:

the denominator 75 can be expressed in the form 5²×3(factors of 75).

if a number has 3 and 5 as its factors, then it will have a terminating decimal expansion.

hence 8/75 has a terminating decimal expansion.

Answer 2

Given : Rational numbers

To Find :   which has terminating decimal expansion

(a) 23/200

(b) 17/9

(c) 8/75

(d) 3/35

Solution:

Rational numbers are terminating decimals or non terminating recurring decimal.

Irrational numbers are non terminating non-recurring decimals

Any Rational number in the form of p/q  where p and q are co primes. where p , q are  integers

if q has only prime factors of 2 and 5 then it is terminating decimal.

if q has prime factors other than 2 and 5 also then its non terminating recurring decimal

(a) 23/200

200 = 2 * 2 * 2 * 5 * 5  

Has only prime factors of 2 and 5

Hence Terminating decimal expansion

17/9

9 = 3 * 3

has factor 3 which is other than 2 and 5  hence  non  terminating recurring decimal expansion

8/75

75 = 3 * 5 * 5

has factors 3  which is other than 2 and 5  hence  non  terminating recurring decimal expansion

3/35

35 = 5 * 7

has factors 7 which is other than 2 and 5  hence  non  terminating recurring decimal expansion

So correct option is a) 23/200

23/200 has a terminating decimal expansion  

23/200 = 0.115

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