Exploring the Real Number System

The video tutorial introduces the real number system, explaining the difference between rational and irrational numbers. It covers rational numbers, which can be expressed as fractions, and irrational numbers, which cannot be expressed as fractions and have non-repeating, non-terminating decimals. The tutorial further explores integers, whole numbers, and natural numbers, illustrating their relationships through a diagram. It provides examples and practice problems to help classify numbers into their respective sets, enhancing understanding of the number system hierarchy.

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

• 2/3

• √3

• 1.5

• 4

What is a rational number?

• A number that cannot be written as a fraction

• A number that can be written as a fraction

• A number that never ends or repeats

• A number that is always positive

Which of the following is a whole number?

• 0

• 1.5

• -3

• √2

Which of the following numbers is a natural number?

• 2

• 0

• 1.5

• -1

In the diagram of the real number system, which subset is the largest?

• Integers

• Real numbers

• Whole numbers

• Natural numbers

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

• -3

• 1.3333...

• √16

• 5/2

What is the simplified form of the square root of 64?

• -64

• -8

• 8

• 64

What is the absolute value of -9?

• -9

• 9

• -1

• 0

Which of the following is a rational number but not an integer?

• 8

• √50

• -11

• 3.895

Where does the number π (pi) belong in the real number system?

• Irrational numbers

• Whole numbers

• Integers

• Rational numbers