Question 1

Which of the following statements about rational numbers is TRUE?

Accepted Answer

Every rational number can be written as a fraction of two integers, where the denominator is nonzero.

Question 2

Which of the following numbers is NOT a rational number?

Accepted Answer

√2

Question 3

Suppose you are asked to find a rational number whose square is exactly 2. What does the material say about this?

Accepted Answer

No such rational number exists.

Question 4

Which of the following is the best description of the set of integers?

Accepted Answer

All positive and negative whole numbers, including zero.

Question 5

Given the table in the material, which value of $$x is $$closest to $$\sqrt{2}$$?

Accepted Answer

1.4

Question 6

Which operation is NOT always closed within the set of rational numbers?

Accepted Answer

Division (when dividing by zero)

Question 7

If $$\frac{m}{n} is a $$rational number, which of the following must be true?

Accepted Answer

$$n 
eq 0$$

Question 8

Which of the following is an example of representing a rational number as a decimal fraction?

Accepted Answer

$$\frac{279}{25} = 11.16$$

Question 9

Why did mathematicians introduce numbers like $$\sqrt{2}$$?

Accepted Answer

Because there are quantities whose squares are not rational numbers.

Question 10

Which of the following is a property shared by both rational numbers and the new numbers like $$\sqrt{2}$$?

Accepted Answer

They can be represented as infinite decimal expansions.

Question 11

If $$x is a $$number such that $$x^2 = 2$, which of the following statements is correct?

Accepted Answer

$$x is $$not a rational number.

Question 12

Which of the following best describes the process of finding $$\sqrt{2} as $$discussed in the material?

Accepted Answer

Assume there is a number between 1.4 and 1.5 whose square is 2.

Question 13

Which of the following is NOT an integer?

Accepted Answer

$$\frac{1}{2}$$

Question 14

Which of the following is a common misconception about rational numbers?

Accepted Answer

All decimal expansions are rational numbers.

Question 15

If $$x = 1.5$$, what is $$x^2$$ according to the table in the material?

Accepted Answer

2.25

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions