Classifying Real Numbers with Venn Diagrams

This video tutorial covers the concepts of rational and irrational numbers, explaining how rational numbers can be expressed as fractions, while irrational numbers cannot. It discusses the characteristics of irrational numbers, such as non-repeating and non-terminating decimals, and provides examples like pi and the square root of non-perfect squares. The tutorial also uses a Venn diagram to illustrate the set of real numbers, which includes both rational and irrational numbers. Finally, it offers practice in classifying numbers into categories such as real, rational, irrational, integers, and whole numbers.

Which of the following is a rational number?

• Pi

• Square root of 2

• 0.75

• Cube root of 5

What is a key characteristic of an irrational number?

• It can be written as a fraction

• It is a repeating decimal

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

• It is a whole number

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

• 2/3

• 5

• 0.5

• Square root of 3

In the Venn diagram of real numbers, which subset includes both rational and irrational numbers?

• Integers

• Natural numbers

• Whole numbers

• Real numbers

Which of the following is a real number but not a whole number?

• 1

• Negative 5

• 21

• 3

What is the classification of the number 0.3 repeating?

• Irrational and real

• Integer and real

• Whole and real

• Rational and real

What is the classification of the number 3.43?

• Rational and real

• Irrational and real

• Whole and real

• Integer and real

What is the classification of the number negative square root of 25?

• Real, rational, and integer

• Real, irrational, and integer

• Real, rational, and whole

• Real, irrational, and whole

What is the classification of the number 16 fourths?

• Real, irrational, and integer

• Real, rational, and whole

• Real, rational, and integer

• Real, irrational, and whole

What is the classification of the number 3 times pi?

• Real and rational

• Integer and irrational

• Real and irrational

• Whole and irrational