Real Numbers
Numbers for Counting and Calculating
Real Numbers are made up of five different types of numbers as described in detail below.
Natural Numbers, more commonly referred to as
Counting Numbers are the numbers children first use to learn to
count objects. They are made up of the numbers 1, 2, 3, 4, 5, 6, 7...
continuing on forever. These counting numbers are represented by the
light blue egg-shaped oval in the above picture.
Whole Numbers are made up of all the Natural Numbers plus zero
(0) = 0, 1, 2, 3, 4, 5, 6, 7... continuing on forever. The Whole Numbers
are represented by the light green egg-shaped oval in the above picture
which includes the Natural Numbers (light blue) oval.
Integers are made up of all the Natural and Whole Numbers plus
their negatives = ...-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,
7... continuing on forever in both directions. The Integers are
represented by the olive green egg-shaped oval in the above picture
which includes both the Whole Numbers (light green oval) and the Natural
Numbers (light blue oval).
Rational Numbers are made up of Ratios of
Integers and are more commonly referred to as fractions. A good way to
remember that Rational Numbers are ratios is to recognize that the word
Ratio is part of the name. Rational Numbers take on the general form of
a/b where a and b can be any Integer except b canNOT be 0. The Rational
Numbers are represented by the pink egg-shaped oval in the picture
above. If b = 1 then a/b = the corresponding Integer. Thus, the
Rational Numbers include all Integers, Whole and Natural Numbers.
Irrational Numbers are made up of special, unique numbers that
canNOT be represented as a ratio of Integers. These numbers when
expressed as decimal numbers do NOT "come out even" and stop and they do
NOT repeat sequences of Whole Numbers. These numbers are represented by
the yellow egg-shaped oval in picture above and do NOT include any of
the previously described numbers. Examples of Irrational Numbers include
the number pi (3.14159265358979...) and the square root of 2
(1.4142135623730950...).
Real Numbers are simply made up of all Rational Numbers and all
Irrational Numbers and are represented by the dark blue egg-shaped oval
in the above picture.
The Real Number System - All the different types of numbers that
make up the Real Number System are summarized in table form in the
picture below. The colors for each number type match the colors of the
egg-shaped ovals in the picture above.
Click Here to go to our Math Dictionary
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