In the division algorithm, if the remainder is zero, then the algorithm terminates, resulting in a terminating decimal. remainder repeats, the calculations that follow will also repeat in a cyclical pattern causing a repeating decimal.
When it comes to deductive reasoning, it is used to reach a logical solution. You start out with the general statement, or hypothesis, and examine all the possibilities so you can reach the final conclusion.
Inductive reasoning is completely opposite - you focus on specific observations, and then make broad generalizations.
