Real Numbers Examples

The pre-requisites to this lesson include the basic understanding of real numbers and its properties.

As we know a real number can be any natural , decimal , fraction , integer or whole number . Below are some such real number examples as well some problems related to them.

Examples of real numbers

1. 0 /100 = 0 (rational , whole , integer)

2. 6 /2 = 3 (rational , natural, positive integer)

3. 3* 2-1 (rational )

4. pi = 3.14159... (irrational)

5. 1/3 = 0.33333…. (rational)

6. (-1)-10 =1 (rational , natural, positive integer)

Algebra Problems

The following problems will further clear your concepts regarding real numbers examples

1. Evaluate 3x2 -2 x -1 where x =1

Solution

Putting value of x in the given expression , we have

3x2 -2 x -1 = 3 (1)2 - 2 (1) -1

= 3(1) – 2 -1

=3 -2-1

=0

So , answer is 0 which is a rational integer and whole number.

2. Evaluate (x3)2 where x = 1

Solution

Putting value of x , we have

(13)2 = ( 1 * 1 *1 )2

= ( 1)2

=1 * 1

=1

So , answer is 1 which is a rational natural number and positive integer.

3. Evaluate (23 * 2-1 * 2)1/2

Solution

Adding the exponents of all the numbers , we have

(23 * 2-1 * 2)1/2 = ( 23 + (-1) +1 )1/2

= ( 23 -1 +1 )1/2

= (21 )1/2

= (21 )1/2

As a number raised to exponent 1/ 2 is equal to its square root , so we have

= = 1.41421356...

So , the answer is 1.41421356... which is irrational number as it is non-terminating and non-recurring.

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