A student claims that the reciprocal of a natural number has a terminating decimal…
MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number
Problem
A student claims that the reciprocal of a natural number n has a terminating decimal expansion of exactly four digits after the decimal point. Investigate this claim as follows:
(i) Show that this situation is possible only when n can be expressed in the form 2a5b, where a and b are non-negative integers.
(ii) Determine all such natural numbers n for which n1 terminates after exactly four decimal places, and state the smallest value of n satisfying this condition.