Exploring the Real Number System

This video tutorial explains the real number system, focusing on the classification of numbers into rational and irrational categories. Rational numbers include natural numbers, whole numbers, integers, fractions, and decimals that terminate or repeat. Irrational numbers are non-repeating, non-terminating decimals, such as pi and non-perfect square roots. The video provides examples and clarifies common misconceptions, helping students understand the organization and classification of numbers in mathematics.

What defines a number as rational?

• It cannot be expressed as a fraction.

• It is a non-terminating decimal.

• It is a non-repeating decimal.

• It can be expressed as a fraction.

What is the smallest natural number?

• -1

• 1

• 2

• 0

Which number set includes zero?

• Natural numbers

• Whole numbers

• Integers

• Irrational numbers

Which of the following is not a characteristic of integers?

• Includes positive numbers

• Includes negative numbers

• Includes zero

• Includes fractions

What type of decimal is considered rational?

• Non-terminating, non-repeating

• Terminating

• Non-terminating, repeating

• Both terminating and repeating

What makes a decimal a terminating decimal?

• It ends after a few decimal places.

• It repeats a pattern.

• It goes on forever without repeating.

• It can be expressed only as a decimal.

What distinguishes a repeating decimal from a terminating decimal?

• It ends after a finite number of decimal places.

• It continues indefinitely with a repeating pattern.

• It is always irrational.

• It cannot be expressed as a fraction.

Why is the square root of 2 considered irrational?

• It is a non-repeating, non-terminating decimal.

• It is a perfect square.

• It is a repeating decimal.

• It can be expressed as a fraction.

Which statement is true about irrational numbers?

• They are always whole numbers.

• They include numbers like the square root of 4.

• They can be expressed as a simple fraction.

• They are non-repeating, non-terminating decimals.

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

• 2/3

• 0.333...

• Pi (π)

• 0.75