Question 1

Which of the following numbers is irrational?

Accepted Answer

√2

Question 2

A student claims that every non-terminating decimal is irrational. Which of the following best evaluates this claim?

Accepted Answer

The claim is incorrect because some non-terminating decimals repeat and are rational.

Question 3

Which of the following numbers has a decimal expansion that is non-terminating and non-repeating?

Accepted Answer

π

Question 4

Which of the following statements about rational numbers is TRUE?

Accepted Answer

All rational numbers can be written as the ratio of two integers with a nonzero denominator.

Question 5

A chemist measures the length of a molecule as 1.4142135 nanometers. Which of the following best describes this number?

Accepted Answer

It is an irrational number because its decimal expansion is non-terminating and non-repeating.

Question 6

Which of the following is NOT a property of rational numbers?

Accepted Answer

The decimal expansion of a rational number is always non-terminating and non-repeating.

Question 7

A patient’s blood glucose level is measured as 0.333... mmol/L (with the 3 repeating). Which type of number best describes this value?

Accepted Answer

Rational

Question 8

Which of the following numbers can be written as a ratio of two integers?

Accepted Answer

−4

Question 9

A historian records the year as −44 (the year of Julius Caesar’s assassination). Which set(s) does this number belong to?

Accepted Answer

Integers and rational numbers

Question 10

Which of the following best explains why √2 is irrational?

Accepted Answer

Because there are no integers m and n (n ≠ 0) such that $$(m/n)^2 = 2.$$

Question 11

A student writes the number 11.16. Which of the following statements is correct?

Accepted Answer

It is a rational number because it can be written as 279/25.

Question 12

Which of the following is a correct classification for the number 0?

Accepted Answer

It is an integer and a rational number.

Question 13

A real-world measurement yields the value 2/4. Which of the following is true about this number?

Accepted Answer

It is rational and can be simplified to 1/2.

Question 14

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

Accepted Answer

It is either terminating or repeating.

Question 15

A student is asked to classify the number −3. Which of the following is the most complete classification?

Accepted Answer

It is an integer and a rational number.

Question 16

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

Accepted Answer

3

Question 17

A medical dosage is calculated as 1.25 mg. Which of the following is true about this number?

Accepted Answer

It is rational because it can be written as 5/4.

Question 18

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

Accepted Answer

Their decimal expansions are non-terminating and non-repeating.

Question 19

A student claims that 0.5 is irrational because it is a decimal. Which of the following best addresses this misconception?

Accepted Answer

0.5 is rational because it can be written as 1/2.

Question 20

Which of the following best describes the relationship between integers and rational numbers?

Accepted Answer

All integers are rational numbers.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions