Question 1

Which of the following numbers is irrational?

Accepted Answer

√2

Question 2

A patient’s temperature is measured as 98.6°F. Which type of number best describes this value?

Accepted Answer

Rational number

Question 3

Which of the following statements about rational numbers is TRUE?

Accepted Answer

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

Question 4

A student claims that 0.121212... (where '12' repeats forever) is an irrational number. Which is the best evaluation of this claim?

Accepted Answer

The claim is incorrect because repeating decimals are rational.

Question 5

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

Accepted Answer

Closed under division by zero

Question 6

A chemist measures the concentration of a solution as 0.70710678... (with no repeating pattern). Which type of number is this most likely to be?

Accepted Answer

Irrational number

Question 7

Which of the following numbers has a terminating decimal representation?

Accepted Answer

11.16

Question 8

A historical record states that a length was measured as exactly 4/3 meters. Which of the following is TRUE about this number?

Accepted Answer

It is a rational number.

Question 9

Which of the following best describes the decimal expansion of an irrational number?

Accepted Answer

Non-terminating and non-repeating

Question 10

A student is asked to find a number x such that $$x^2 = 2. $$Which of the following is correct?

Accepted Answer

x is an irrational number.

Question 11

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

Accepted Answer

0

Question 12

A medical dosage is calculated as 2.75 mg. Which of the following statements is correct?

Accepted Answer

2.75 is a rational number with a terminating decimal.

Question 13

Which of the following numbers CANNOT be written as a fraction of two integers?

Accepted Answer

π

Question 14

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

Accepted Answer

The claim is incorrect because repeating decimals are rational.

Question 15

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 16

A scientist records a measurement as 0.666... (where 6 repeats forever). Which of the following is TRUE?

Accepted Answer

This is a rational number with a repeating decimal.

Question 17

Which of the following is a property shared by all integers?

Accepted Answer

They are rational numbers.

Question 18

A student is given the decimal 0.142857142857... (where '142857' repeats forever). Which of the following is TRUE?

Accepted Answer

This is a rational number with a repeating decimal.

Question 19

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

Accepted Answer

Every number is either rational or irrational, but not both.

Question 20

A real-world measurement is recorded as 3.141592653... (with no repeating pattern). Which of the following is TRUE about this number?

Accepted Answer

It is an irrational number.

Numbers and Functions: Foundations for Calculus

Study Guide - Practice Questions