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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
Also called counting numbers. {1, 2, 3, 4, …}
Whole Numbers
Includes 0 and the natural numbers. {0, 1, 2, 3, 4,…}
Integers
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 fraction
Decimals:
Terminating:
A decimal with a finite number of digits.
A decimal that stops.
Nonterminating:
An infinite number of digits either with a
repeating pattern or not repeating.
Rational numbers
Number sets
Irrational 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.
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
Sample: 5.1231231231…
An irrational number between –4 and -2
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.
Sample: 2.4545454545…
An irrational number between 1 and 2.
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.
5 5
18  18
Review
How is the following read?
AB
Segment AB
What does the following mean?
AB
Measure of
segment AB
Example
Find BE
2 1
1 
3 3
 2  2
Find CF
1  2   3  3
Find AD
2  1
1
1
 2     2  2
3  3
3
3
Find BG
2
2
1
1
1  2   4  4
3
3
3
3
Homework
Pg. 53 1- 10 all, 12 – 36 E