SOLUTION: Classify the given numbers as real and rational, real and irrational, or complex. Justify your answer. Remember you may need to simplify BEFORE you classify! 1. (3)1/2

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Real numbers come in two kinds, rational and irrational. Rational numbers are those that can be expressed as the ratio of two integers, ratio being the root of the word rational. Irrational numbers cannot be expressed as the ratio of two integers. ALL decimal representations are rational - which means to say that you cannot exactly represent an irrational number with a decimal no matter how precise you choose to make the representation. Also, just because you cannot represent a decimal equivalent of a number exactly, doesn't mean the number is irrational. If the decimal repeats, it is rational.

Complex numbers are numbers of the form

where

and

are real numbers and

is the imaginary number defined by

. Note that if

is zero, you just have a real number, but if

is zero, you still have a complex number with a zero real part.

Super Double Plus Extra Credit:

Select any two rational numbers on the number line, no matter how small the distance between them. How many irrational numbers exist between your two selected numbers?

John