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

Why did the ancient Greeks conclude that √2 is not a rational number?

Accepted Answer

Because there is no fraction m/n such that $$(m/n)^2 = 2.$$

Question 4

Which of the following is the best description of an integer?

Accepted Answer

Any whole number, including positive numbers, zero, and negative numbers.

Question 5

Given the table below, what can you conclude about the value of √2?

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

Accepted Answer

√2 is between 1.4 and 1.5.

Question 6

Which of the following operations does NOT always result in a rational number when performed on two rational numbers?

Accepted Answer

Division (when the divisor is zero)

Question 7

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

Accepted Answer

11.16

Question 8

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

Accepted Answer

There is no rational number z such that $$z^2 = 2.$$

Question 9

Which of the following is NOT an integer?

Accepted Answer

2.5

Question 10

If a number can be written as an infinite decimal expansion that eventually repeats, what type of number is it?

Accepted Answer

A rational number

Question 11

Which of the following best explains why 279/25 is a rational number?

Accepted Answer

It can be written as a ratio of two integers.

Question 12

Which of the following is a property shared by all rational numbers?

Accepted Answer

They can be expressed as a fraction of two integers with a nonzero denominator.

Question 13

Which of the following is an example of a negative integer?

Accepted Answer

-2

Question 14

If you add two rational numbers, which of the following is always true?

Accepted Answer

The result is a rational number.

Question 15

Which of the following best describes the set of numbers known as 'integers'?

Accepted Answer

All positive and negative whole numbers, including zero.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions