Have attempted on numerous occasions to get the concept of rational numbers to click over the course of this past week. A solution for this problem would be appreciated.

Part (c) of this problem is literally just a check to see if you know the definition of rational number. As much as I don't like to advocate for doing math by rote memorization, there are just certain things there's no choice but to memorize - and the definitions of terms is one of them.

Recall that the definition of a rational number is a number which can be written as the ratio (for these purposes you can consider that interchangeable with the word fraction) of two integers (aka whole numbers).

By additionally recalling that dividing by some number is the same as multiplying by the reciprocal ("1 over") that number, you can begin to play with this definition and find some useful rules. Specifically, suppose you have some rational number x. By definition you can write:

• x = a/b

for some pair of whole numbers a and b. But you can also write:

• x * b = a

In other words, a given number is rational if you can multiply it by some whole number and get another (not necessarily different) whole number as a result.

I'll go ahead and tell you that all the answer choices you've checked so far are indeed rational numbers, but now you have to ask yourself: Are there any of the remaining unchecked answer choices that you can transform into a whole number by multiplying? (Hint: multiplying by 10 is the same as moving the decimal point one place to the right)

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