Number Systems

• Irrational Numbers
  • Irrational numbers are those which cannot be expressed in the form , where p, q are integers and q ≠ 0.

Example: are irrational numbers.

 

• • Irrational numbers are the numbers which neither terminate nor repeat.

Example:  or as 3.14, both of which are rationals.

• Decimal expansion of a rational number can be of two types:

(i) Terminating

(ii) Non-terminating and repetitive

In order to find decimal expansion of rational numbers we use long division method.

For example, to find the decimal expansion of .

We perform the long division of 1237 by 25.

 

Hence, the decimal expansion of is 49.48. Since the remainder is obtained as zero, the decimal number is terminating.

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