Decimal Representation of Real Numbers

We have seen that Real Numbers include both Rational and Irrational Numbers.

But how do these numbers appear when we write them in decimal form?

Consider:

The decimal ends after a finite number of digits.

Such a decimal is called a terminating decimal.

Now consider:

The decimal does not end, but the digit 3 keeps repeating.

This is called a non-terminating recurring decimal.

Now look at an Irrational Number:

Its decimal representation does not end and does not repeat in a fixed pattern.

This is called a non-terminating non-recurring decimal.

THE PATTERN

Rational Numbers have decimal representations that either terminate or eventually repeat.

Irrational Numbers have decimal representations that continue forever without repeating.