Decimal Representation of Irrational Number 

When an irrational number is changed into a decimal, the resulting number is a nonterminating, nonrecurring decimal.

For example, consider the decimal representation of √2:

Decimal Representation of Irrational Number

Therefore, √2 = 1.4142.... It is nonterminating. It is also nonrecurring asat every stage the remainder is different.

Thus, the irrational number √2 is represented as a nonterminating, nonrecurring decimal.

 

Note: The approximate value of π = 22/7 (or 3.14). Actually, π is a non-terminating, nonrecurring decimal number and so π is also an irrational number.




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