Question 1

Consider the set $$M = \{-1028, -\frac{2050}{5}, -\frac{3}{25}, 0, \frac{4}{21}, 1, \sqrt{24}, 11, 9\pi\}. $$Which of its elements are irrational numbers?

Accepted Answer

$$\sqrt{24}, 9\pi$$

Question 2

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

Accepted Answer

Rational numbers can be written as fractions, while irrational numbers cannot be written as fractions.

Question 3

Given $$\sqrt{24}$$, which of the following is true?

Accepted Answer

$$\sqrt{24} is an $$irrational number because it cannot be written as a fraction.

Question 4

Which of the following numbers is irrational?

Accepted Answer

$$\pi$$

Question 5

If $$x = 9\pi$$, which of the following statements is correct?

Accepted Answer

$$x is $$irrational because $$\pi is $$irrational and multiplying by 9 does not change that.

Question 6

Which of the following sets contains only rational numbers?

Accepted Answer

$$\{-1028, -\frac{2050}{5}, -\frac{3}{25}, 0, \frac{4}{21}, 1, 11\}$$

Question 7

Which of the following is NOT a rational number?

Accepted Answer

$$\sqrt{24}$$

Question 8

A student claims that $$-\frac{2050}{5} is $$irrational because it is negative. Is this claim correct?

Accepted Answer

No, $$-\frac{2050}{5} is $$rational because it can be written as a fraction.

Question 9

Which of the following numbers can be written as a terminating decimal?

Accepted Answer

$$-\frac{3}{25}$$

Question 10

If $$x = \sqrt{24}$$ and $$y = 9\pi$$, which of the following statements is true?

Accepted Answer

Both $$x$$ and $$y$$ are irrational numbers.

Question 11

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

Accepted Answer

$$0 is a $$rational number.

Question 12

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

Accepted Answer

$$11$$

Question 13

Which of the following numbers is a non-integer rational number?

Accepted Answer

$$\frac{4}{21}$$

Question 14

If a number can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are integers and $$b 
eq 0$$, what type of number is it?

Accepted Answer

Rational number

Question 15

Which of the following numbers is irrational because it is a non-repeating, non-terminating decimal?

Accepted Answer

$$\pi$$

Identifying Irrational Numbers in a Set

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