Real Numbers

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

The union of the set of rational numbers and irrational numbers forms the set of real numbers.

Q = {rational numbers}

= {irrational numbers}

Then = R = {real numbers}

To represent a rational number on the number line

Mark the following rationals on the number line:

To represent an irrational number on the number line

To mark , an irrational number, on the number line.

Let OA = AB = 1 unit and

Then in rt.

= 1 + 1

Cut off OP = OB = on the number line.

Then, the point P represents on the number line.

Using Pythagoras' theorem in rt.

OB = , if AO = 2 and AB = 1

Cut off OP = OB =

Then the point P represents on the number line.

In the same way can be represented on the number line.

(i) For every real number, there is a corresponding point on the number line.

(ii) For every point on the number line, there exists a real number.

Express with rational denominator.

Express with rational denominator.