Lesson 2-1 Real Numbers and Number Lines

Ohio Content Standards:

Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

Whole Numbers

Includes zero and the Natural Numbers

Whole Numbers Includes zero and the Natural Numbers Natural Numbers are also called the Counting Numbers

Integers

Includes zero, the positive integers, and the negative integers

Rational Numbers

Any number that can be written as a fraction

Rational Numbers Any number that can be written as a fraction Terminating Decimals are rational

Rational Numbers Any number that can be written as a fraction Terminating Decimals are rational Repeating Decimals are rational

Irrational Numbers

Decimals that are nonterminating and do not repeat

Real Numbers

Include both rational and irrational numbers

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.

For each situation, write a real number with ten digits to the right of the decimal point.

A rational number between 6 and 8 with a 2-digit repeating patternA rational number between 6 and 8 with a 2-digit repeating pattern

For each situation, write a real number with ten digits to the right of the decimal point. A rational number between 6 and 8 with a 2-digit repeating patternA rational number between 6 and 8 with a 2-digit repeating pattern An irrational number greater than 5An irrational number greater than 5

Coordinate

Number that corresponds to a point on a number line

Origin

Has coordinate zero

Postulate 2-2 Distance Postulate

For any two 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 two points is the positive difference of the corresponding numbers.

Absolute Value

Number of units a number is from zero on the number line.

Absolute Value Number of units a number is from zero on the number line. Symbol : two vertical slashes

Use the number line to find CE AGFEDCB

Erin traveled on I-85 from Durham, North Carolina, to Charlotte. The Durham entrance to I-85 that she used is at the 173-mile marker, and the Charlotte exit she used is at the 39-mile marker. How far did Erin travel on I-85?

Assignment: Pgs evens, evens