Concept Map

Real Numbers

I.       Irrational Numbers

1.real number that is not rational: any real number that cannot be expressed as the exact ratio of two integers, e.g. v2 and p.
Numbers that cannot be expressed as an exact ratio are called irrational numbers; numbers that can be expressed as an exact ratio are called rational numbers. For instance, 1/2 (one half, or 50 percent of something) is rational. 1.61803 (), 3.14159 (p), 1.41421 (2 ), are irrational. History claims that Pythagoras in the sixth century b.c.e. first used the term when he discovered that the square root of 2 could not be expressed as a fraction.

A.    Decimals to not end or repeat

B.    They go on for infinity

II.   Rational
Numbers

1.whole number: a whole number or the quotient of any whole numbers, excluding zero as a denominator. Rational numbers contain everything except real and irrational numbers. They contain proper and improper fraction, terminating decimals, and the denomination cannot be zero, but fractions are allowed.
.

A.    Fractions

1.    Denomination cannot be zero

2.    Proper or Improper Fraction

B.    A termination Decimal

III.    Natural Numbers

The whole numbers from 1 upwards: 1, 2, 3, and so on ...
Or from 0 upwards in some fields of mathematics: 0, 1, 2, 3 and so on ...
No negative numbers and no fractions.
The natural numbers are the ordinary numbers, 1, 2, 3, etc., with which we count. They are sometimes called the counting numbers. They have been called natural because much of our experience from infancy deals with discrete (separate; individual; easily countable) objects such as fingers, balls, peanuts, etc.

A.        Counting
Numbers

B.    Does not include zero

IV.    Whole Numbers

1.number without fractions: a positive or negative number, including zero, that does not contain a fraction or decimal. Whole numbers are also known as your natural counting numbers, they are the numbers that most children learn first when learning their numbers.

A.    Include Zero

B.    Counting Numbers

V.     Integers

- any rational number that can be expressed as the sum or difference of a finite number of units, being a member of the set …-3, -2, -1, 0, 1, 2, 3…
- an individual entity or whole unit.
The integers on the left side of zero (0) are called negative numbers, and are represented by a negative sign (-) placed before them, as in -5, -10, and -15.* The integers on the right side of 0 are called positive numbers. Examples include 5, 10, and 15. The positive integers are known as counting numbers or natural numbers. The positive integers and 0 are called whole numbers. Zero is an integer but it is neither positive nor negative.

A.    Positive Numbers

B.            Negative Numbers