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The Properties of Number Systems

The Properties of Number Systems. 6.5. Counting Numbers. Numbers used to count things. There are infinitely many counting numbers Examples : 1, 2,3,4,5,6. Not including zero! . Whole Numbers. Zero and all of the counting numbers make up whole numbers.

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The Properties of Number Systems

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  1. The Properties of Number Systems 6.5

  2. Counting Numbers • Numbers used to count things. • There are infinitely many counting numbers Examples: 1, 2,3,4,5,6. • Not including zero!

  3. Whole Numbers • Zero and all of the counting numbers make up whole numbers. • There are no negative whole numbers!! Examples: • 0, 1,2,3,4,5,6,7,8,….

  4. Integers • All the whole numbers and their opposites make up the set of integers. Examples: • -5,-4,-3,-2,-1,0,1,2,3,4,5 • Zero is an integer!!!

  5. Rational Numbers • Any number that can be written as a simple fraction (a/b) where a and b are integers and b = 0. • Rational numbers can be positive, negative, or 0. • They can be whole numbers because any whole number can be expressed as a fraction. 3= 3/1.

  6. Rational numbers continued.. • They can also be mixed numbers or a percent because any mixed number or percent can be renamed as a fraction. Examples: • ½ • 2.5 • -4 ½ • 1/3 • 0

  7. Terminating Decimals • The word “terminate” means “end”. • A decimal that ends is a terminating decimal. • In other words, a terminating decimal doesn’t keep going. A terminating decimal will have a finite number of digits after the decimal point.

  8. Terminating Decimals Examples: • ½ = 0.5 • 8/10 = .8 • ¼ = 0.25

  9. Repeating decimal • The decimal goes on for infinity. • Not only does the digit go on or continue, but they do in a repeating pattern. Examples: • 1/3= 0.33333333333333 • 2/3= 0.66666666666 • 1/7 = 0.142857142857

  10. Irrational Numbers • Non terminating decimals whose digits do not follow a repeating pattern. Examples: • √2 • ∏=3.14159265389

  11. REAL NUMBERS • Rational numbers • Integers • Whole numbers • Counting numbers • Irrational numbers

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