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Definition of Terminating And Non Terminatin

 NONTERMINATING DECIMALS 

 Every rational number can be expressed either as a terminating decimalor as a non-terminating decimal.From the topic"Definition of terminating and non -terminating decimals " first we see what is a terminating decimal ? the word terminate means "end" . so the definitionof terminating decimal is nothing but "the decimal that ends " and the decimal that do not ends is a non terminating decimal.From  the definition of terminating and non terminating decimals it is clear that when we divide a whole number by any number if we get the reminder zero after some divisions,then it is a terminating decimal .If the remainder is not zero and is equal to a fixed and repeated number  after repeatingthe divisions then it is a  non terminating decimal.

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definition of terminating and non terminating - examples

let us take an example for terminating and non terminating decimal.

ex 1:

1/8=0.125

inthe  above example the division is exact. that mean no remainder is left. the quotients of such divisions are called terminating

decimals

example 2:

4/9=0.44444.........

in above example the division never ends,it continues. The quotient of such divisions are called non-terminating decimals.

From the definition of terminating and non terminating ,it is clear that in terminating decimals the division is exact and in

non -terminating decimals division  it continues.From the deffinition of terminating decimals and non-terminating decimals

ifthe denominator of a rational number can be expressed as the power either of 2 or  5 or 2 and 5 both, the rational numbers can be convertedinto terminating decimal.

for example 24/25  is convertible into terminating decimal.

in a rational number    2/3=0.6666666.........it is recurring decimal.


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definition of terminating and non terminating - Conclusion

Accordingto the deffinition of terminating decimals and non terminating decimalsit is named as non repeating decimals and repeating decimals respectively.  We can also call recurring decimals as non -terminating decimals  and non-recurring decimals as terminating decimals.