Which of the following has a decimal equivalent that is a terminating

Question

Which of the following has a decimal equivalent that is a terminating decimal?

I. 1/128
II. 1/225
III. 1/384

A. I only
B. II only
C. I and II
D. I and III
E. I, II and III

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Kunal.lost · Accepted Answer

A fraction ends in a terminating decimal only if the denominator has 2 and 5 as its prime factors.

1/128 = 2^7 
1/225 = 5^2 x 3^2
1/384 = 2^7 x 3

Out of the three fractions, only the first one satisfies our condition.

So the answer would be  A. I only

ManifestDreamMBA · Answer

For a fraction to be terminating, in simplest form, it's denominator must be of the form 2^n * 5 ^m

Given all of the fractions are in simplest form, focusing on denominator

I. 1/128 = 1/2^7
Terminating  ✅

II. 1/225 = 1/25*9
Non-Terminating  ❌

III. 1/384
384 is divisible by 3, Non-Terminating  ❌

Answer A

Sketchitesh · Answer

Condition for temination decimal:  If a fraction can be expressed with a denominator that has " only"  the prime factors 2 and/or 5 (or powers of 2 and/or 5)

128= 2^7
225=  3^2 * 5^2 
 384 = 2^7 * 3

Only 128 satisfies our condition hence  A is correct.

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Ayeka · Answer

I. 1/128 =1/2^7.........Terminating 
II. 1/225 =1/(5^2)*(3^2)....... non terminating 
III. 1/384 =1/(2^7)*(3)...........non terminating 
Only (I) is terminating

Answer: A

Dereno · Answer

Terminating decimal is one when the denominator  reduced to the lowest form  contains the factors as   ONLY    prime numbers   2 and 5.

I. 1/128

128 on prime factorisation = 2^7. Since it contains only factors of 2, it’s a terminating decimal.

II. 1/225

225 =15^2 = 5^2* 3^2 . It’s  not  a terminating decimal. Since it contains factor 3.

III. 1/384

384 is also not a terminating decimal. As it contains factors other than 2 and 5.

ONLY I holds good.  Option A

NextstopISB · Answer

A fraction will have a terminating decimal if and only if its denominator (in simplest form) has no prime factors other than 2 and/or 5.

I. 1/128 → 128 = 2^7 → Only prime factor is 2 → Terminating

II. 1/225 → 225 = 3^2 × 5^2 → Includes factor 3 → Not terminating

III. 1/384 → 384 = 2^7 × 3 → Includes factor 3 → Not terminating

Answer: A. I only

rohitz98 · Answer

From the given options
I) 1/128 is equivalent to 1/(2^7). It has only 2 in denominator hence its terminating decimal
II) 1/225 is equivalen to 1/(15 ^2) which has both powers of 5 and 3. Hence its not a terminating one
III) 1/384 has a power of 3 in its denominator. Hence not terminating

Hence  Option A

Abhiswarup · Answer

Option I= 1/128it is terminating decimal

Option II =1/225 225=15*15 =3*3*5*5
1/9 is not a terminating decimal

Option III = 1/384, 384=3*128, 1/3 is not terminating decimal

Thus option I is only terminating. Answer is A

Which of the following has a decimal equivalent that is a terminating

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GMAT Problem Solving (PS) Questions

Which of the following has a decimal equivalent that is a terminating

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