The Real Number System

• are decimals that never end... think Pi

• are non-perfect square roots

• ARE ALSO REAL NUMBERS

• CANNOT BE RATIONAL NUMBERS. 

• can be written as a fraction (1/2)

• are decimals that have a repeating pattern (1.32323232...)

• are decimals that terminate (2.75)

• are ALL numbers that aren't irrational (like 3 or -57).

• ARE ALSO REAL NUMBERS

• CANNOT BE IRRATIONAL.

• Integers

• Whole Numbers

• Natural Numbers

• are counting numbers on a number line. This includes negative numbers.

• do not include decimals or fractions.

• ARE ALSO RATIONAL NUMBERS AND REAL NUMBERS.

Every number on the number line is an integer. 

• Include POSITIVE integers

• includes ZERO

• DO NOT include negative integers

• do not include decimals or fractions

• ARE ALSO INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.

Whole numbers start at 0 and include every positive integer on the number line. 

• include the integers on a number line STARTING AT 1.

• DO NOT include 0.

• DO NOT include negative numbers. 

• DO NOT include fractions and decimals

• ARE ALSO WHOLE NUMBERS, INTEGERS, RATIONAL NUMBERS, AND REAL NUMBERS.

Natural numbers start at 1 and include every positive integer on the number line. 

• order of values does not matter

• 7+8=8+7

• (9*4)+6=6+(9*4)

• 5*4=4*5

• The grouping of values does not matter! Move parentheses.

• (a+b)+c=a+(b+c)
  

• (5+1)+3=5+(1+3)

• Stays the same!!

• a+0=a

• b*1=b

• 4(1)=4

• 3+0=3

• uses the opposite to "cancel" a value!

• a+(-a)=0

• 3*(1/3)=1

• Multiply a value to an expression inside parentheses. 

• a(b+c)=ab+ac

• 2(x+6)=2x+12