The real number system includes rational numbers such as integers, fractions, and terminating or repeating decimals. It also includes irrational numbers like square roots and pi. Real numbers can be classified into different subsets including integers, rational numbers, irrational numbers, natural numbers, whole numbers, and fractions.

1. Real
Number
System
The set of numbers that
we use in arithmetic is
called the set of real
numbers (ℝ).

2. Terminating Decimals Repeating Decimals
0.25
0.20
0.333…
0.555…
or 0.3
or 0.5

4. 0.1010010001…
4.353353335….
-3.10100100010000…

5. Set of Real Numbers and their
relationship of each other
Real Number (R)
Irrational Number Rational Number
Fraction Integer
Whole Number

6. Identify the sets to which each of the following
numbers belongs by marking the appropriate boxes.
Number Integer Natural
Number
Rational
Number
Irrational
Number
Whole
Number
Real
Number
-9 Yes No Yes No No Yes
No No Yes No No Yes
5 Yes Yes Yes No Yes Yes
No No No Yes No Yes
Yes Yes Yes No Yes Yes
0 Yes No Yes No Yes Yes

7. Identify the sets to which each of the following
numbers belongs by marking the appropriate boxes.
Number Integer Natural
Number
Rational
Number
Irrational
Number
Whole
Number
Real
Number
2.721 No No Yes No No Yes
2π No No No Yes No Yes
Yes No Yes No No Yes
0.10100… No No No Yes No Yes
330 Yes Yes Yes No Yes Yes
1.232 No No Yes No No Yes