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

If $$x is a $$rational number, which operation will always result in a rational number (provided the operation is defined)?

Accepted Answer

Addition, subtraction, multiplication, and division (except division by zero)

Question 4

Which of the following best describes the set of integers?

Accepted Answer

All positive and negative whole numbers, including zero

Question 5

Why is $$\sqrt{2}$$ considered an irrational number?

Accepted Answer

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

Question 6

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

Accepted Answer

$$\frac{279}{25} = 11.16$$

Question 7

Suppose you are given a number $$x$$ such that $$x^2 = 2$. Which of the following statements is correct?

Accepted Answer

$$x is $$irrational because it cannot be written as $$\frac{m}{n}$$ for integers $$m$$ and $$n.$$

Question 8

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

Accepted Answer

Their square roots are always rational.

Question 9

A student claims that $$\frac{1}{3} is $$not a rational number because its decimal expansion is $$0.333...$$ and never ends. Is this claim correct?

Accepted Answer

No, because $$\frac{1}{3} is $$rational and its decimal expansion repeats.

Question 10

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

Accepted Answer

$$-4$$

Question 11

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 12

Which of the following is a correct statement about the algebraic rules for irrational numbers like $$\sqrt{2}$$?

Accepted Answer

They obey the same algebraic rules as rational numbers, such as $$a + b = b + a.$$

Question 13

Which of the following is the best definition of a real number according to the study material?

Accepted Answer

A number that can be represented as an infinite decimal expansion.

Question 14

Given the fraction $$\frac{1116}{100}$$, which of the following is its decimal representation?

Accepted Answer

$$11.16$$

Question 15

Which of the following is a property of the set of integers?

Accepted Answer

It is closed under addition, subtraction, and multiplication.

Question 16

A chemist measures the length of a molecule as $$1.414$$ nanometers. Which of the following is closest to the actual value of $$\sqrt{2}$$?

Accepted Answer

$$1.414$$

Question 17

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

Accepted Answer

Zero is both an integer and a rational number.

Question 18

If $$x is a $$number such that $$x^2 = 2$, which interval does x$ lie in according to the study material?

Accepted Answer

$$1.4 \u003c x \u003c 1.5$$

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions