Question

Which of the following statements is true if p is an integer and q is a nonzero integer?

Answer 1

The answer is A, I just got finished doing that quiz and i got it right so lol its A for sure.

Explanation:

Answer 2

Note: Sets of Rational Numbers

Therefore, the answer is

Note:

(1) Any number that can be written as a fraction is RATIONAL

(2) Any number that CANNOT be written as a fraction is not Rational

(3) Examples of rational numbers

`(4)/(2),(3)/(5),(1)/(10),-(5)/(4),...`

(4) Example of Irrational Numbers

`√(2),√(11),tan1,log5,e^2`

(5). How to differentiate decimal numbers that is rational from the Irrational numbers

Example 1: Which is rational and which is Irrational

`\begin{gathered} 0.666666666666667 \\ and \\ 0.4771212547 \end{gathered}`

Answer: (a). If the decimal can be converted to fraction, then it is rational, but if it can't be converted to fraction, then it is irrational

(b). The decimal of a rational number (or fraction) most times repeat it's digit.

Now, for the above question

`\begin{gathered} 0.666666666666667\text{ =}(2)/(3) \\ So\text{ it is rational} \\ Notice\text{ the repetition of digits} \end{gathered}`

and

`\begin{gathered} 0.4771212547 \\ The\text{ digits does not follow any repetition pattern} \\ There\text{ is no fraction this decimals can represent} \\ So\text{ it is not Rational} \\ It\text{ is an Irrational number} \\ Indeed,\text{ } \\ 0.4771212547=log\mleft(3\mright) \end{gathered}`