Real Numbers and their Decimal Expressions

Real Numbers

All numbers including both rational and irrational numbers are called Real Numbers.

\mathrm{R = - 2, -\left(\dfrac{2}{3}\right)},0,3 and \sqrt2

Real Numbers and their Decimal Expansions

1. Rational Numbers

If the rational number is in the form of \mathrm{\dfrac{a}{b}} then by dividing a by b we can get two situations.

a. If the remainder becomes zero

While dividing if we get zero as the remainder after some steps then the decimal expansion of such number is called terminating.



b. If the remainder does not become zero

While dividing if the decimal expansion continues and not becomes zero then it is called non-terminating or repeating expansion.



It can be written as 0.\overline3

Hence, the decimal expansion of rational numbers could be terminating or non-terminating recurring and vice-versa.

2. Irrational Numbers

If we do the decimal expansion of an irrational number then it would be non –terminating non-recurring and vice-versa. i. e. the remainder does not become zero and also not repeated.


\pi= 3.141592653589793238……

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