Another representation of rational numbers aside from fractions is the decimal form. Every fraction has a decimal representation:
, , and .
Notice that some of the fractions above are terminating, while the others are repeating decimals. The fractions and have only one decimal place, while and have infinitely many (Can you see why?). Now, given a fraction, can we determine if it’s a terminating or non-terminating decimal without dividing?
First let us examine the characteristics of terminating decimals, say 0.125. The easiest way to convert this decimal into fraction is by dividing a whole number by a power of 10: Continue reading