The real number system includes all numbers that can be found on the number line, consisting of rational and irrational numbers. Rational numbers can be expressed as a quotient of two integers, while irrational numbers cannot be expressed as such a quotient and are represented by non-repeating, non-terminating decimals. Real numbers thus encompass all integers, fractions, and irrational numbers on the infinite number line.

1. Real Number System

2. Real Number
 A real number is any number that can be found on
the number line.
The rational numbers and irrational numbers
combined form the real numbers.
-1 1 2 3 40-2-3-4
-0.25-1
𝟏
𝟐
-2.66
__ 𝟑
𝟒 𝟐 𝟑
𝟏𝟏

3. Real Numbers
Rational
Numbers
Irrational
Numbers
Integers Fractions
Negative
Integers
Zero Positive Integers /
Counting Numbers
Whole Numbers

4. Rational Numbers
Rational Number is a number that can be
expressed as a quotient
𝑎
𝑏
of two integers. The
integer a is the numerator while the integer b,
which cannot be 0, is the denominator.

5. Counting Numbers or
Natural Numbers
These are the numbers we use in counting
things {1,2,3,4,5,6, …}
(The Three dots, called ellipsis, Indicate that
the pattern continues indefinitely.)

6. Whole Numbers
These are counting numbers
together with 0. That is 0, 1, 2,
3, 4, 5, 6, …

7. Integers
These are whole numbers together with
the negative counting numbers that is,
… , -3, -2, -1, 0, 1, 2, 3, …
0 1 2 3 4 5 6 7-5 -2-4 -3 -1-6-7
ZERONegative numbers Positive numbers

8. Irrational Numbers
 Irrational Number or irrational is a number
that cannot be expressed as a quotient
𝑎
𝑏
of two
integers. Every irrational number may be
represented by a decimal that neither repeats
nor terminates.
Examples are 2, 5, 3,
3
7,
3
6, and so on.