
Look, punk, we're talking "pure mathematics" here. The actual numbers are equivalent, assuming we're speaking decimal here. The use of trailing zeros does indeed imply confidence in the measurement technique used to acquire the extra zeros, but that does not affect the actual number.
Equality is by definition a reflexive, symmetric, and transitive relation on the set under consideration, in this case the set C of all complex numbers and its subset R, consisting of all real numbers.
Go up to any gradeschool, high school, or college mathematics professor/teacher and ask him/her to verify that 3.14160 = 3.1416. This will establish the initial hypothesis. Now, by the definition of symmetry on a set relation, we can "reverse" the statement, showing that 3.1416 = 3.14160.
Oh, and I'll help you take Regis down if you can prove that all even integers > 2 are expressible as the sum of two prime integers. 
