Question

Which is the only fraction that must be represented by a non terminating decimal?

a. 7/5
b. 7/4
c. 7/3
d. 7/2

Answer 1

The answer is:
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[C]: 7/3 .
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Note: Anything divided by "3" that does not result in an integer is ALWAYS going to result in a value containing a non-terminating decimal.

Answer 2

The correct option is C) 7/3.

Explanation:

Consider the provided numbers.

If the rational number can be written in the form of
`(p)/(2^n* 5^m)` then the rational number will be a terminating decimal.

Now consider the provided options:

Option A) 7/5 can be written as:
`(7)/(2^0* 5^1)`

Thus it is a terminating decimal.

Option B) 7/4 can be written as:
`(7)/(2^2* 5^0)`

Thus it is a terminating decimal.

Option C) 7/3 can be written as:
`(7)/(2^0* 5^0* 3^1)`

Thus it is not a terminating decimal.

Option D) 7/2 can be written as:
`(7)/(2^1* 5^0)`

Thus it is a terminating decimal.

Hence the only fraction that must be represented by a non terminating decimal is 7/3.

The correct option is C) 7/3.