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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let us take an example for terminating and non terminating decimal.
inthe above example the division is exact. that mean no remainder is left. the quotients of such divisions are called terminating
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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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.