Question

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

Answer 1

for any rational no. the condition satisfied is of denominator is of form 2∧n5∧m to have terminating decimal expansion

Answer 2

Sol : 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 / 100 = 0.1 ( 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^m x 5^m )


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^m x 5^m ).


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 ).