Exploring the Real Number System in SOL 8.2

The video tutorial reviews the real number system, focusing on rational and irrational numbers. It explains how irrational numbers like pi have non-repeating, non-terminating decimals, while rational numbers can be expressed as fractions with repeating or terminating decimals. The tutorial also covers integers, whole numbers, and natural numbers, emphasizing their differences. It guides viewers on identifying and classifying numbers within the real number system and evaluates true or false statements about number properties. Finally, it discusses repeating and terminating decimals, providing examples and clarifications.

What is a characteristic of irrational numbers?

• They have a repeating decimal pattern.

• They are always whole numbers.

• They can be expressed as a fraction.

• Their decimal representation never ends or repeats.

Which statement about irrational numbers is true?

• They are always positive.

• They have a non-repeating, non-terminating decimal expansion.

• They can be written as a simple fraction.

• They include the number zero.

Which of the following is an example of a rational number?

• Square root of 2

• Square root of 87

• 1/3

• Pi (π)

What does it mean if a number is an integer?

• It is always a fraction.

• It can be any whole number, positive, negative, or zero.

• It cannot be a whole number.

• It must be a positive whole number.

Which number set does zero belong to?

• None of the above

• Irrational numbers

• Whole numbers

• Natural numbers

Which of these numbers is not a whole number?

• 5

• 0

• 10

• -3

Which of the following numbers is considered a natural number?

• 2/7

• 0

• 6.0

• -3

Identify the false statement about rational numbers.

• They can have a terminating decimal.

• They include the number pi (π).

• They can have a repeating decimal pattern.

• They can be expressed as a fraction.

What classification describes a number that can be expressed as a fraction?

• Natural

• Rational

• Integer

• Irrational

Which of the following is an example of an irrational number?

• Square root of 12

• Square root of 81

• 2/7

• 0.333...