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Question

Write the condition for a rational number which can have a terminating decimal expansion. 


Solution

 The condition required for a rational number to have a terminating decimal expansion is that when the number is in its simplest form then its denominator should be in the form of 2^m x 5^n ( where m and n are any whole number ).

Have a look at few examples :

a.) 10 / 200 = 0.05 ( In this we can find that when the fraction will be broken down into its simplest form then its denominator will be in the form of 2^2 x 5^1 )


b.) 9 / 90 = 0.1 ( Well it also have a terminating decimal expansion as when it will be broken down then its denominator will be in the form of 2^1 x 5^1 ).


c.) 9/81 = 0.11111111111......... ( 9/81 has a non terminating decimal expansion because when we shall break it into its simplest form then it won't be in the form of 2^m x 5^n)

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