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

1. \(\frac{1}{2}\)
2. \(\frac{1}{10^2} \)
3. \(\frac{1}{2^{10}}\)

1. I only
2. II only
3. I and II
4. I and III
5. II and III

Correct Answer: (E)

Approach Solution : 1

If and only if b (denominator) has the shape 2^n 5^m, where m and n are non-negative integers, the reduced fraction a/b (which indicates that fraction has already been reduced to its lowest term) can be expressed as a terminating decimal.
For instance, 7/250 is a terminating decimal of the form 0.028 because 250 (denominator) equals 2*(5^3). Because 3/30 = 1/10 and the denominator 10 = 2*5, the fraction 3/30 is also a terminating decimal.
It should be noted that whether or not the fraction is reduced does not matter if the denominator already contains only 2-s and/or 5-s.
The terminating decimal, for instance, will always be x/(2^n 5^m), where x, n, and m are integers.
If the denominator of the prime is anything other than 2 or 5, we need to reduce it to see if it can be reduced. For instance, the denominator of the fraction 6/15 has the prime number 3, and we need to recognise if it can be reduced.
Now let us look at the question,

1. 1/12 = 1 / [(2^2)*3]
2. 1/10^2 = 1 / [(2*5)^12]
3. 1/(2^10)

Therefore only II and III will be terminating decimals.

Approach Solution : 2

Any number divided by 2, 5, or the combination of 2 and 5 (10) would be a terminating decimal .
1/2 = 0.5
1/5 = 0.2
1/10 = 0.1
1/50 = 0.02 etc..
Only the values from II and III fit this requirement and so they are the answers.

“Which of the following has a decimal equivalent that is a” - is a subject that the GMAT quantitative reasoning section covers. A school needs to be proficient in a variety of qualitative skills to answer the GMAT Problem Solving questions correctly. There are 31 questions in the GMAT Quant section as a whole. The GMAT Quant topics' problem-solving section calls for the resolution of calculative mathematical puzzles.

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