applied geometry lesson 2 – 1 real numbers and number lines objective: learn to find the distance...
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Applied GeometryLesson 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, …}
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…}
Number sets…Rational numbers:
Any number that can be written as a fractionDecimals:
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
Number setsIrrational Numbers: a number that is nonterminating and nonrepeating.
Examples?0.1234567…0.17117111711117… pattern but not a repeating pattern.
3.141592…
2 8
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.
ExamplesFor 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.
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…
Number lines
Coordinate: the number that corresponds to a point on a number line.
Origin: 0 on a number line
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.
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 positive difference of the corresponding numbers.
Absolute Value
Absolute value: the number of units a number is from zero on a number line.
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Review
How is the following read?
What does the following mean?
AB
AB
Segment AB
Measure of segment AB
Example
Find BE
Find CF
Find AD
Find BG
3
1
3
21 22
3321
3
12
3
12
3
1
3
22
3
14
3
14
3
22
3
21
Homework
Pg. 53 1- 10 all, 12 – 36 E