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 property is true for all rational numbers a and b (with b   0)?

Accepted Answer

Their sum, difference, product, and quotient (except division by zero) are all rational numbers.

Question 4

Why is 2 not a rational number?

Accepted Answer

Because it cannot be written as a fraction of two integers.

Question 5

Which of the following is the correct decimal representation of 27925?

Accepted Answer

11.16

Question 6

Suppose m and n are integers with n   0. Which equation must be true for mn to be the square root of 2?

Accepted Answer

mn2=2

Question 7

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

Accepted Answer

-2

Question 8

If x is a number between 1.4 and 1.5 such that x2=2, what type of number is x?

Accepted Answer

An irrational number

Question 9

Which of the following statements is true about the set of integers?

Accepted Answer

It includes all positive and negative whole numbers, and zero.

Question 10

Which of the following is a property of rational numbers but NOT of all real numbers?

Accepted Answer

They can always be written as a fraction of two integers.

Question 11

A student claims that 2 can be written as 75. Which of the following best explains why this is incorrect?

Accepted Answer

Because 2 is not a rational number and cannot be written as a fraction of two integers.

Question 12

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

Accepted Answer

It is always a rational number.

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 always irrational.

Question 14

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

Accepted Answer

It always terminates or repeats.

Question 15

Which of the following is NOT an integer?

Accepted Answer

12

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions