Real Numbers for Class 10

Real Numbers ®

Combination of Rational numbers (Q) and Irrational numbers (Q^I) are called Real Numbers. These are denoted by R

Before going to know about Real numbers, recall previous numbers.

1.Natural numbers (N)

Counting numbers are called Natural numbers.

These are denoted by N.

These numbers are start with 1.

So 1 is the smallest natural number.

There is No ending (Last) number in natural numbers.

So there is No greatest number in natural numbers.

N = {1, 2, 3, 4, 5, 6, …………………. }

Every number is one more than its previous number except 1.

2.Whole Numbers (W)

Natural numbers including zero (0) are called Whole Numbers.

These are denoted by W.

These numbers are start with 0.

So zero (0) is the smallest Whole number.

There is No ending (Last) number in Whole numbers also.

So there is No greatest number in Whole numbers.

 W = {0, 1, 2, 3, 4, 5, 6, …………………. }

Every number is one more than its previous number except 0.

Whole number set is contained all Natural numbers.

So Natural number set is Subset to Whole number set.

3.Integers (I/Z)

Combination of Positive numbers and Negative numbers including zero (0) are called Integers.

These are denoted by I or Z.

 (Z is taken from the German word “Zahl”, which means number)

There is No starting (First) number and ending (Last) number in Integers.

So there is No smallest number and No greatest number in Integers.

 Z = {…….…..-4, -3, -2, -1, 0, 1, 2, 3, 4 ……….}

Every negative number is less than Zero.

And every negative number is also less than positive numbers.

Integer number set is contained all Natural numbers and Whole numbers.

So Natural number set and Whole number set are Subsets to Integers.

N ⊂ W ⊂ Z 

4.Rational numbers (Q)

The numbers, which can be written in the form of p/q (where p, q are integers and q≠0) are called Rational numbers.

These are denoted by Q.

Q = {p/q, p, q are integers and q≠0}

N ⊂  W ⊂ Z ⊂ Q

5. Irrational numbers (Q^l)

The numbers, which cannot written in the form of p/q (where p, q are integers and q≠0) are called Irrational numbers.

These are denoted by Q^l.