Lesson on the Real Number System

Natural (Counting) Numbers

​Natural numbers are a part of the number system, including all the positive integers from 1 to infinity. Natural numbers are also called counting numbers because they do not include zero or negative numbers. They are a part of real numbers including only the positive integers, but not zero, fractions, decimals, and negative numbers.

​Examples - 1,2,3,4,5,6,7,8,9,10......

Multiple Choice

Which group only contains natural numbers?

• 0, -2, 0.5

• 8, $$\frac{1}{2}$$ , -3

• 5, 2, 14

• 0.1, $$\frac{2}{3}$$ , 9

Whole Numbers

Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are a subset of the whole numbers.

Examples - 0,1,2,3,4,5,6,7,8,9,10....

Multiple Choice

Which of the following is NOT a whole number?

• 0

• 3

• 0.4

• 12

Integers

​

An integer is a number with no decimal or fractional part, from the set of negative and positive numbers, including zero.

• Positive Integers: An integer is positive if it is greater than zero. Example: 1, 2, 3 . . .

• Negative Integers: An integer is negative if it is less than zero. Example: -1, -2, -3 . . .

• Zero is defined as neither negative nor positive integer. It is a whole number.

​Examples: ... -3,-2,-1,0,1,2,3 ...

Multiple Choice

Which of the following is an integer?

• $$\frac{1}{2}$$  

• 0.53

• -9

• -1.6

Rational Numbers

A Rational Number can be made by dividing an integer by an integer. (They make a ratio/ fraction)

​Rational numbers stop or end

Rational numbers can be made into a fraction

Rational numbers can repeat

Rational numbers are perfect square roots​

​Examples:

​

Irrational Numbers

Irrational numbers are those real numbers that cannot be represented in the form of a ratio.

​Irrational numbers do not stop or end

Irrational numbers cannot be made into fractions​

Irrational numbers do not ​repeat

Irrational numbers are not perfect square roots ​

​Examples:

Multiple Choice

Which of the following is Rational?

• $$\pi$$  

• $$\sqrt[]{5}$$  

• 0.7196432.....

• $$0.\overline{9}$$  

Multiple Choice

Which of the following is Irrational?

• 8

• $$\sqrt[]{4}$$  

• 0.67

• $$\pi$$