1 / 21

The Number System

The Number System. The Complex Number System and Operations with Numbers. Repeating Decimals. Repeating decimals are decimals that contain a infinite number of digits. Examples: 0.333… 7.689689… FYI…The line above the decimals indicate that number repeats. Terminating Decimals.

abie
Download Presentation

The Number System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Number System The Complex Number System and Operations with Numbers

  2. Repeating Decimals • Repeating decimals are decimals that contain a infinite number of digits. • Examples: • 0.333… • 7.689689… FYI…The line above the decimals indicate that number repeats.

  3. Terminating Decimals • Terminating decimals are decimals that contain a finite number of digits. • Examples: • 36.8 • 0.125 • 4.5

  4. The Complex Number System • All numbers in the world • Represented by ℂ

  5. Imaginary Numbers Imaginary numbers are all the numbers that deal with the square root of a negative number and contain the letter i in it. Example: You will learn more about these numbers in Algebra 2

  6. Real Numbers • Real numbers consist of all numbers that can be represented on a number line. • Represented by ℝ

  7. Irrational Numbers • Irrational numbers are any numbers that cannot beexpressed as . • They are expressed as non-terminating, non-repeatingdecimals; decimals that go on forever without repeating a pattern. • Examples of irrational numbers: • 0.34334333433334… • 45.86745893… • (pi)

  8. Rational Numbers • Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b ≠ 0. • They can always be expressed by using terminating decimals or repeating decimals. • Represented by ℚ • Examples:

  9. Integers • Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…} • Represented by ℤ

  10. Whole Numbers • Whole numbers are the set of numbers that include 0 plus the positive numbers. {0, 1, 2, 3, 4, 5,…} • Represented by 𝕎

  11. Natural Numbers • Natural numbers are the set of counting numbers. {1, 2, 3,…} • Represented by ℕ or ℙ

  12. Venn Diagram of the Complex Numbers ComplexNumbers Real Numbers Imaginary Numbers Rational Numbers Integers Irrational Numbers WholeNumbers NaturalNumbers

  13. Example • Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. • 117 • 0 • -12.64039… • -½ • 6.36 • -3

  14. FYI…For Your Information • When taking the square root of any number that is not a perfect square, the resulting decimal will be non-terminating and non-repeating. Therefore, those numbers are always irrational.

  15. Properties of Real Numbers Property Addition Multiplication Commutative a+b= b+aab= ba Associative (a+b)+c = a+(b+c)(ab)c = a(bc) Identity a + 0 = a a•1 = a Inverse a + (-a) = 0 a = 1 Opposite Reciprocal Distributive Property a(b + c) = ab + ac

  16. Examples of Properties Name the property displayed: • -2 + (x – 5) = (-2 + x) – 5 2. (-2) ( -½ ) = 1 3. 2(4 – 5) = (4 – 5)2 4. x(y – w) = xy – xw

  17. Order of Operations • Parenthesis/Grouping Symbols • Exponents • Multiplication and Division – left to right • Addition and/or Subtraction – left to right

  18. Grouping Symbols Grouping symbols include parenthesis, braces, brackets, numerators and denominators of fractions and underneath a radical or inside absolute value symbols.

  19. Examples – Using Order of Operations Evaluate the following: • 22(12 + 8) 5 2. 52 ÷ (2 + 11) 3. 7 • 12 + 30 ÷ 5

More Related