Question 1

Which of the following statements is TRUE about rational numbers?

Accepted Answer

Every rational number can be written as a fraction $$\frac{m}{n}$$, where $$m$$ and $$n$$ are integers and $$n 
eq 0.$$

Question 2

Which of the following numbers is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 3

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 4

Which of the following is the best description of an irrational number based on the study material?

Accepted Answer

A number that cannot be written as a fraction of two integers.

Question 5

Given the decimal expansion $$11.16$$, which of the following is a correct fractional representation?

Accepted Answer

$$\frac{279}{25}$$

Question 6

Which of the following sets includes all the others?

Accepted Answer

The set of real numbers

Question 7

If $$x is a $$rational number and $$y is a $$rational number, which of the following must also be a rational number?

Accepted Answer

$$x + y$$

Question 8

Which of the following is an example of a number that is not an integer but is a rational number?

Accepted Answer

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

Question 9

Why did the ancient Greeks conclude that $$\sqrt{2} is $$not a rational number?

Accepted Answer

Because there is no fraction $$\frac{m}{n} of $$integers such that $$\left(\frac{m}{n}\$$right)^2$$ = 2$$

Question 10

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

Accepted Answer

Division, if $$b = 0$$

Question 11

Suppose you are given the decimal $$1.44. $$Which of the following numbers squared gives this value?

Accepted Answer

$$1.2$$

Question 12

Which of the following best describes the set of integers?

Accepted Answer

All positive and negative whole numbers, including zero

Question 13

If $$x is a $$number such that $$x^2 = 2$ and 1.4$$ \u003c x \u003c 1.5$$, which of the following is the best estimate for x$?

Accepted Answer

$$1.414$$

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

Zero is a rational number.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions