Question 1

Which of the following numbers has a non-terminating, non-repeating decimal expansion?

Accepted Answer

√2

Question 2

A patient’s medication dosage is calculated as 1.5 mg per kg of body weight. If the patient weighs exactly √2 kg, which type of number best describes the total dosage?

Accepted Answer

Irrational number

Question 3

Which of the following statements about rational numbers is TRUE?

Accepted Answer

Every integer is a rational number.

Question 4

A chemical solution requires exactly 0.125 liters of a reagent. Which type of number is 0.125?

Accepted Answer

Rational number

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 student claims that the decimal 0.272727... is irrational because it never terminates. What is the flaw in this reasoning?

Accepted Answer

Repeating decimals are always rational.

Question 7

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

Accepted Answer

It cannot be expressed as a ratio of two integers.

Question 8

A historical mathematician is trying to find a rational number whose square is 2. Which of the following best describes the outcome of this search?

Accepted Answer

No such rational number exists.

Question 9

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

Accepted Answer

0

Question 10

A real-world measurement yields a value of 11.16. Which of the following could be a possible fraction representation for this value?

Accepted Answer

279/25

Question 11

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

Accepted Answer

All rational and irrational numbers.

Question 12

A student is asked to classify the number -4. Which of the following is the most accurate classification?

Accepted Answer

Integer

Question 13

Which of the following decimal expansions represents a rational number?

Accepted Answer

0.666...

Question 14

A scientist records a measurement as 1.4142135... and notes that it never repeats or terminates. What can be concluded about this number?

Accepted Answer

It is an irrational number.

Question 15

Which of the following is a property shared by both rational and irrational numbers?

Accepted Answer

They both belong to the set of real numbers.

Question 16

A function is defined on all real numbers. Which of the following inputs would NOT be valid for this function?

Accepted Answer

None of the above

Question 17

A student is asked to approximate √2 by squaring numbers between 1 and 2. Which of the following is the best estimate based on the table provided?

Accepted Answer

1.4

Question 18

Which of the following is an example of a number that is NOT a real number?

Accepted Answer

√−1

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 historian notes that the discovery of irrational numbers challenged the ancient Greek understanding of numbers. Which mathematical fact best illustrates this challenge?

Accepted Answer

Some numbers, like √2, cannot be written as a ratio of two integers.

Numbers and Functions: Foundations for Calculus

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