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:

a)23/200

Step-by-step explanation:

because

23/200= 0.115

17/9 = 1.88888.... upto infinity

8/75 = 0.108888.... upto infinity

3/35 = 0.0857142857142857142...upto infinity

Answer 2

Solution :-

we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

So, checking prime factors of given options we get,

a) 23/200

→ Denominator = 200 = 2 * 2 * 2 * 5 * 5

since prime factors of denominator are 2 and 5 only . The given fraction is a terminating decimal expansion .

b) 17/9

→ Denominator = 9 = 3 * 3

since prime factors of denominator is other than 2 and 5 . The the given fraction is a non - terminating decimal expansion .

c) 8/75

→ Denominator = 75 = 3 * 5 * 5

since prime factors of denominator is other than 2 and 5 . The the given fraction is a non - terminating decimal expansion .

d) 3/35

→ Denominator = 35 = 5 * 7

since prime factors of denominator is other than 2 and 5 . The the given fraction is a non - terminating decimal expansion .

Hence, option (a) 23/200 is a terminating decimal expansion .

Learn more :-

(3) निम्न के स्थानीय मान लिखिये-

(अ)43.24

(स)884.20

(ब) 534.34

(द) 178.34

https://brainly.in/question/37666224