Question 1

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Which statement best describes the set of integers?

Accepted Answer

All whole numbers, including zero and negative numbers

Question 3

Why is $$\sqrt{2}$$ not a rational number?

Accepted Answer

Because it cannot be written as a fraction of two integers

Question 4

Which of the following is an example of a rational number?

Accepted Answer

$$\frac{-2}{3}$$

Question 5

If $$x is a $$rational number and $$y is a $$rational number (with $$y 
eq 0$$), which of the following is always true?

Accepted Answer

$$x \div y is $$rational

Question 6

Which of the following statements is TRUE about the number zero?

Accepted Answer

Zero is an integer and a rational number

Question 7

Given the decimal $$11.16$$, which of the following fractions is equivalent to it?

Accepted Answer

$$\frac{1116}{100}$$

Question 8

Which of the following is NOT a property of rational numbers?

Accepted Answer

They can be squared and the result is always irrational

Question 9

Suppose you are asked to find a number $$x$$ such that $$x^2 = 2$. Which of the following is closest to x$?

Accepted Answer

$$1.4$$

Question 10

Which of the following best describes the decimal expansion of a rational number?

Accepted Answer

It always terminates or repeats

Question 11

A student claims that $$\frac{1}{3} is $$not a rational number because its decimal expansion is $$0.333...$$ and never ends. What is the error in this reasoning?

Accepted Answer

A rational number can have a repeating decimal expansion

Question 12

Which of the following is an example of an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 13

If $$x is a $$rational number and $$y is an $$irrational number, which of the following is always true?

Accepted Answer

$$x + y is $$irrational

Question 14

Which of the following numbers can be written as an infinite non-repeating decimal?

Accepted Answer

$$\sqrt{2}$$

Question 15

Which of the following is a correct statement about the sum of two rational numbers?

Accepted Answer

It is always rational

Question 16

Which of the following best explains why $$\sqrt{2} is $$assumed to exist, even though it cannot be written as a fraction?

Accepted Answer

Because there is a number between 1.4 and 1.5 whose square is exactly 2

Numbers and Functions: Foundations of Calculus

Study Guide - Practice Questions

Study Guide - Flashcards