Before, I discuss the misconceptions, let us recall the definition of rational numbers. A rational number is a number that can represented by the fraction where and are integers and not equal to 0. From this definition and other previously learned concepts, let us examine the following misconceptions about rational numbers.
Misconception 1 : Zero is not a rational number.
Truth: YES, it is. Zero, and negative and positive integers are all rational numbers. For example, , , and are all fractions whose numerators and denominators are integers and denominator 1 (which is clearly not equal to 0). » Read more
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: » Read more