Math 8 Unit 1-The Number System

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WHOLE NUMBER

The Numbers from 0 to +α

NATURAL NUMBER

The Numbers 1 to +α

Also known as Counting Numbers

INTEGER

The set of whole numbers and their opposites
From -α to +α

RATIONAL NUMBER

A number that can be written as a/b where a and b are integers, but b is not equal to 0. .25=¼

IRRATIONAL NUMBER

A number whose decimal form is non-terminating and non-repeating. Cannot be written in the form a/b, where a and b are integers (b cannot be zero).

REAL NUMBER

The set of all rational and irrational numbers.

DECIMAL

A number that is written using the base-ten place value system. 5.6

DECIMAL EXPANSION

Representing a number in decimal form.
¾=.75

REPEATING DECIMAL

A number whose decimal representation eventually repeats the same sequence of digits. 1/3=.3333333...

NON-TERMINATING DECIMAL

A decimal numeral that does not end in an infinite sequence of zeros. 1.42345426343517189191........

TERMINATING DECIMAL

Has a decimal expansion that ends in zero. 0.726500000 = 0.7265

RATIO

A comparison of two quantities by division.
½ or 1 to 2 or 1:2

APPROXIMATION

A result that is not necessarily exact, but is within the limits of accuracy required for a given purpose.
146 ≈ 150 2.57≈3

GREATER THAN

When a number is larger than the other number.
65 > 56

LESS THAN

When a number is smaller than the other number. 107 < 215

RADICAL

The symbol √ which is used to respresent the square root

SQUARE ROOT

A number that when multiplied by itself, equals the given number.

CUBE ROOT

A number that when multiplied by itself, and then mulitplied by itself again equals the given number.

CUBED

A number cubed is the number raised to the third power.

PERFECT SQUARE

A number with integers as its square roots.
1,4,9,16,25....

PERFECT CUBE

A number that can be written as the cube of an integer. 1,8,27,64....

PYTHAGOREAN THEOREM

In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse, a²+b²=c²

CONVERSE

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

PROOF

a²+b²=c² where c is the hypotenuse while a and b are the legs of the triangle.

LEGS

The two sides of a right triangle that form the right angle. ( called a and b)

HYPOTENUSE

The side of the right triangle that is opposite the right angle ( called c)

COUNTER EXAMPLE

An example that shows a conjecture is false.

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