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Applied Geometry

Applied Geometry. Lesson 2 – 1 Real Numbers and Number Lines. Objective: Learn to find the distance between two points on a number line. Number sets. Natural Numbers Whole Numbers Integers. Also called counting numbers. {1, 2, 3, 4, …}.

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Applied Geometry

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  1. Applied Geometry Lesson 2 – 1 Real Numbers and Number Lines Objective: Learn to find the distance between two points on a number line.

  2. Number sets • Natural Numbers • Whole Numbers • Integers Also called counting numbers. {1, 2, 3, 4, …} Includes 0 and the natural numbers. {0, 1, 2, 3, 4,…} Includes 0, negative #s, and positive #s {…-4, -3, -2, -1, 0, 1, 2, 3, 4…}

  3. Number sets… Any number that can be written as a fraction • Rational numbers: Decimals: Terminating: Nonterminating: A decimal with a finite number of digits. A decimal that stops. An infinite number of digits either with a repeating pattern or not repeating. Rational numbers

  4. Number sets • Irrational Numbers: a number that is nonterminating and nonrepeating. • Examples? 0.1234567… 0.17117111711117… pattern but not a repeating pattern. 3.141592…

  5. Postulate 2-1 • Number Line Postulate: • Each real number corresponds to exactly one point on a number line. • Each point on a number line corresponds to exactly one real number.

  6. Examples For each situation, write a real number with 10 digits to the right of the decimal point. • A rational number less than 10 with a 3-digit repeating pattern • An irrational number between –4 and -2 Sample: 5.1231231231… Sample: -3.1211211121… *Make sure you include the ‘…’ to show that it is nonterminating. Make sure you have 10 digits on the right.

  7. Examples • A rational number greater than –10 with a 2 digit repeating pattern. • An irrational number between 1 and 2. Sample: 2.4545454545… Sample: 1.8988988898…

  8. Number lines • Coordinate: the number that corresponds to a point on a number line. • Origin: 0 on a number line

  9. Postulate 2-2 • Distance Postulate: For any 2 points on a line and a given unit of measure, there is a unique positive real number called the measure of the distance between the points.

  10. Postulate 2-3 • Ruler Postulate: Points on a line are paired with the real numbers, and the measure of the distance between the 2 points is the positivedifference of the corresponding numbers.

  11. Absolute Value • Absolute value: the number of units a number is from zero on a number line.

  12. Review • How is the following read? • What does the following mean? Segment AB AB Measure of segment AB

  13. Find BE Find CF Find AD Find BG Example

  14. Homework • Pg. 53 1- 10 all, 12 – 36 E

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