without actually performing the long division state whether 17 / 3125 will have a terminating decimal expansion or a non-terminating decimal expansion​

Answer:It is terminating decimal expansion.Step-by-step explanation:17/3125 is a terminating decimal expansion.REASON:If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.Proof:Lets have a look on the solution of the given term.17/1325We will break the denominator in the factors:If we multiply 5 five times than it will give us 1325.17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5We know that any number with exponent zero = 1∴ 2^0 = 1So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.Thus this term has a terminating decimal expansion....