applied geometry lesson 2 – 1 real numbers and number lines objective: learn to find the distance...

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.

55 1818

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