Question 1

Which of the following statements best describes a rational number?

Accepted Answer

A number that can be written as a fraction of two integers, with a nonzero denominator.

Question 2

Which of the following numbers is NOT a rational number?

Accepted Answer

2

Question 3

Which set of numbers includes all positive integers, zero, and negative integers?

Accepted Answer

Integers

Question 4

Why is 2 considered an irrational number?

Accepted Answer

Because there is no fraction mn such that mn2 = 2.

Question 5

Which of the following is a correct decimal representation of a rational number?

Accepted Answer

11.16

Question 6

If mn is a rational number, which operation is NOT always guaranteed to result in another rational number?

Accepted Answer

Division by zero

Question 7

Given the table below, which value of x is closest to 2?

| x   | $$x^2$$  |
|-----|------|
| 1.4 | 1.96 |
| 1.5 | 2.25 |

Accepted Answer

1.4

Question 8

Which of the following statements about the set of rational numbers is TRUE?

Accepted Answer

The product of two rational numbers is always rational.

Question 9

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

Accepted Answer

It always terminates or repeats.

Question 10

Suppose you are asked to find a number between 1.4 and 1.5 whose square is exactly 2. What type of number are you looking for?

Accepted Answer

An irrational number

Question 11

Which of the following is an example of a number that is both an integer and a rational number?

Accepted Answer

0

Question 12

Which of the following is NOT a property shared by all rational numbers?

Accepted Answer

They can be divided by zero.

Question 13

A student claims that 1116100 is a rational number. Which of the following justifies this claim?

Accepted Answer

It can be written as a fraction of two integers with a nonzero denominator.

Question 14

Which of the following best explains why 2 is not a rational number?

Accepted Answer

There is no integer solution to m2 = 2n2.

Question 15

Which of the following is a true statement about the number zero?

Accepted Answer

Zero is an integer and a rational number.

Question 16

If you add a rational number and an irrational number, what type of number is the result (in general)?

Accepted Answer

Always irrational

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions