Can there be more than one type of number?
Yes, numbers can be classified as more than one type, and it’s not always easy to keep them
straight. The following lists some ways to better understand the plethora of number types:
- A rational number is not always an integer: 4/1 is an integer, but 2/3 is not;
but an integer is always a rational number because it can be represented by
a fraction by putting the integer over 1, or /1, such as 2/1 or 234/1 - A number can either be rational or irrational but not both
- The number for pi (3.141592 ...) is irrational (the decimal does not repeat)
and real - 0.25 is considered rational (the numbers terminate) and real
- The fraction 5/3 is rational (it’s a fraction) and real
- The number 10 can be explained using many terms, including a counting
number, whole number, integer, rational, and real
How do regularand non-regular numbersdiffer?
Regular and non-regular numbers are actually other terms for rational numbers. Reg-
ular numbers are positive integers that have a finite decimal expansion. In other
words, a number that seems to “end.” For example, one quarter (1/4) is equal to the
decimal equivalent of 0.25 in which the numbers end with “5.” A non-regular number
is one that includes repeating decimals—numbers that seem to go on forever. For
example, one third (1/3) is equal to the decimal equivalent of 0.3333... in which the 3s
go on indefinitely. 75
MATH BASICS
What are imaginary numbers?
T
he “opposite” of real numbers are (logically enough) called imaginary num-
bers. In particular, they are all non-zero multiples (real numbers) of the square
root of 1, which is also represented as i,with the formula defined as follows:i 1
then i^2 ( 1 )^2 1The 1 does not have a position on a number line; and no number can be
squared to get 1. (If you square a positive number, the result is positive; if you
square a negative number, the result is also a positive number.) Thus, in order to
square a number to get a negative one, mathematicians invented the imaginary
number, i.