Exploring Rational and Irrational Numbers

The video tutorial introduces the concept of rational numbers, explaining their place within the broader category of real numbers. It covers subcategories such as whole numbers, integers, and natural numbers, providing definitions and examples for each. The tutorial then delves into rational numbers, describing them as numbers that can be expressed as fractions, terminating decimals, or repeating decimals. It contrasts these with irrational numbers, which cannot be written as fractions and include non-repeating, non-terminating decimals. The video concludes with a comparison of rational and irrational numbers, offering examples to solidify understanding.

Which of the following is a subset of real numbers?

• Abstract numbers

• Fictional numbers

• Rational numbers

• Imaginary numbers

What characteristic do whole numbers have?

• They are always irrational

• They include fractions

• They have no decimal part

• They can be negative

Which of these is a property of whole numbers?

• They start from zero

• They include negative numbers

• They can have decimals

• They are always fractions

Which of these numbers is considered an integer?

• Pi

• 3/4

• -3

• 2.5

Which statement about integers is correct?

• They include fractions

• They can only be positive

• They include both positive and negative numbers, including zero

• They are a type of irrational number

Natural numbers start from which number?

• 0

• -1

• 1

• 2

A rational number can be expressed as:

• a fraction a/b where b is not zero

• a never-ending decimal

• a square root of a prime number

• a non-repeating decimal

What makes a number rational?

• It can be written as a fraction with a non-zero denominator

• It is a perfect square

• It is a repeating decimal only

• It cannot be expressed as a fraction

Which of the following is a characteristic of irrational numbers?

• They cannot be decimals

• They are always positive

• They have decimals that never end or repeat

• They can be written as a fraction

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

• -8

• Pi

• 4.0

• 2/3