Question

Write whether the rational number 7/75 will have a terminating decimal expansion or anor-terminating repeating decimal expansion.

Answer 1

a no. has a terminating decimal expansion in case it can be expressed in the form p/q where q can be expressed in the form 2^n*5^m....
7/75 will have a non terminating repeating decimal expansion...
because 75=5*5*3
here the decimal expansion of 75 is not of the req. form....
Hence, so.