Question

Qi.
Which of the following will have a terminating decimal expansion?
(a) 77/210
(b) 23/30
(c) 125/441
(d)23/8​

Answer 1

Answer:

d) 23/8

Step-by-step explanation:

For terminating decimal expansion, denominator must have only 2 or only 5 or 2 and 5 as factor

23/8=23/(2)^3

(only2 as factor of denominator so terminating)

HOPE IT HELPS U........

Answer 2

23/8 has terminating decimal expansion as denominator has only 2 as a factor

Given:

• Rational Numbers
• (a) 77/210
• (b) 23/30
• (c) 125/441
• (d)23/8​

To Find:

• Which will have terminating decimal Expansion.

Solution:

• Rational numbers are real numbers which can be written in the form p/q where p and q are integers and q≠0
• Any number in the form of p/q  where p and q are co primes.
• 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
• Rational numbers are terminating decimals or non terminating recurring decimal.
• Irrational numbers are non terminating non-recurring decimals

Check each option one by one.

Step 1:

77/210

Divide numerator and denominator by 7

11/30

11 and 30 are co prime

30 = 2 x 3 x 5

Has 3 as one factor Hence non terminating recurring decimal Expansion

Step 2:

23/30

23 and 30 are co prime

30 = 2 x 3 x 5

Has 3 as one factor Hence non terminating recurring decimal Expansion

Step 3:

125/441

125 = 5 x 5 x 5

441 = 3 x 3 x 7 x 7

No common Factors hence co prime

Denominator 3 and 7  as one factor Hence non terminating recurring decimal Expansion

Step 24:

23/8

23 and 8 are co primes

8 = 2 x 2 x 2

Denominator has only 2  as  factor Hence  terminating decimal Expansion

23/8 has terminating decimal expansion

23/8 = 2.875

Correct option is d) 23/8

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