Question 1

Which of the following numbers is NOT a rational number?

Accepted Answer

√2

Question 2

A patient’s medication dosage is calculated as 1.414 mg, which is an approximation of √2 mg. Why is this value only an approximation?

Accepted Answer

Because √2 is an irrational number and cannot be written exactly as a fraction.

Question 3

Which of the following statements is TRUE about rational numbers?

Accepted Answer

They can be written as the ratio of two integers, with a nonzero denominator.

Question 4

A chemist needs to measure exactly 11.16 mL of a solution. Which of the following best describes this number?

Accepted Answer

It is a rational number because it can be written as a fraction.

Question 5

Which of the following decimal expansions represents an irrational number?

Accepted Answer

1.4142135...

Question 6

A historian is analyzing the year -44 (the assassination of Julius Caesar). Which set does -44 belong to?

Accepted Answer

The set of integers and rational numbers

Question 7

Which of the following is a property of rational numbers?

Accepted Answer

The product of two rational numbers is always rational.

Question 8

A student claims that 0.101001000100001... (where the number of zeros between the ones increases by one each time) is a rational number. Is this claim correct?

Accepted Answer

No, because the decimal does not terminate or repeat.

Question 9

Which of the following best explains why all integers are rational numbers?

Accepted Answer

Because every integer can be written as a fraction with denominator 1.

Question 10

A medical researcher records a measurement as 1.333... mg. Which of the following is TRUE about this number?

Accepted Answer

It is rational because it is a repeating decimal.

Question 11

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

Accepted Answer

0

Question 12

A real-world measurement is given as 2.718281828... (the decimal expansion of e). Which of the following is TRUE?

Accepted Answer

It is an irrational number because its decimal expansion does not repeat or terminate.

Question 13

Which of the following is the best approximation for √2 based on the table provided in the study materials?

Accepted Answer

1.4

Question 14

A student says that every non-terminating decimal is irrational. Which of the following is a counterexample?

Accepted Answer

0.333333...

Question 15

Which of the following statements about real numbers is correct?

Accepted Answer

All real numbers can be represented as infinite decimal expansions.

Question 16

A financial analyst is working with the number 0.25. Which of the following is TRUE?

Accepted Answer

It is a rational number because it terminates.

Question 17

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

Accepted Answer

The square root of every rational number is rational.

Question 18

A scientist records a measurement as -2.5. Which sets does this number belong to?

Accepted Answer

Rational numbers and real numbers

Question 19

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

Accepted Answer

It always repeats or terminates.

Question 20

A student is asked to classify the number -7. Which of the following is correct?

Accepted Answer

It is an integer and a rational number.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions

Study Guide - Flashcards