Question 1

Which of the following numbers is irrational?

Accepted Answer

√2

Question 2

A student claims that every decimal expansion that terminates or repeats is a rational number. Which of the following best evaluates this claim?

Accepted Answer

The claim is correct because all such decimals can be written as a ratio of two integers.

Question 3

Which of the following statements about the number zero is TRUE?

Accepted Answer

Zero can be written as 0/1, making it a rational number.

Question 4

A nurse needs to measure out exactly 1.5 mL of a medication. Which of the following best describes 1.5 as a number?

Accepted Answer

It is a rational number because it can be written as 3/2.

Question 5

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

Accepted Answer

The square root of every rational number is rational.

Question 6

Suppose you are given a number whose decimal expansion is 0.123456789101112... (where the digits are written in order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...). Which of the following is TRUE about this number?

Accepted Answer

It is an irrational number because its decimal expansion neither terminates nor repeats.

Question 7

A chemist needs to prepare a solution with a concentration of exactly 2/3 mol/L. Which of the following statements is correct about 2/3?

Accepted Answer

2/3 is a rational number because it is a ratio of two integers.

Question 8

Which of the following best describes the set of real numbers?

Accepted Answer

All rational and irrational numbers.

Question 9

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

Accepted Answer

Integers and rational numbers

Question 10

Which of the following numbers has a decimal expansion that neither terminates nor repeats?

Accepted Answer

√2

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 always irrational.

Question 12

A patient’s temperature is measured as 98.6°F. Which of the following statements is correct about this number?

Accepted Answer

It is a rational number because it can be written as 493/5.

Question 13

Which of the following is a correct statement about the square root of 2?

Accepted Answer

It is an irrational number.

Question 14

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

Accepted Answer

0

Question 15

A student claims that every integer is a rational number. Which of the following best supports this claim?

Accepted Answer

Every integer can be written as a fraction with denominator 1.

Question 16

Which of the following best describes the decimal expansion of 1/7?

Accepted Answer

It repeats after a certain point.

Question 17

A real-world measurement is recorded as 0.101001000100001... (where the number of zeros between the ones increases by one each time). Which of the following is true about this number?

Accepted Answer

It is an irrational number because its decimal expansion neither terminates nor repeats.

Numbers and Functions: Foundations for Calculus

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