Lesson 2-1 Real Numbers and Number Lines. Ohio Content Standards:

Lesson 2-1Lesson 2-1Real Numbers and Number

Lines

Ohio Content Standards:

Ohio Content Standards:• Apply properties of operations and the

real number system, and justify when they hold for a set of numbers.

Whole 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

Integers

• Includes zero, the positive integers, and the negative integers

Rational Numbers

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

Irrational Numbers

• Decimals that are nonterminating and do not repeat

Real Numbers

Real Numbers

• Include both rational and irrational numbers

Postulate 2-1Number Line Postulate

Postulate 2-1Number 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.

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

• An irrational number greater than 5An irrational number greater than 5

Coordinate

Coordinate

• Number that corresponds to a point on a number line

Origin

Origin

• Has coordinate zero

Postulate 2-2Distance Postulate

Postulate 2-2Distance 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

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

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.

-3 -2 -1 0 1 2 3

A GFEDCB

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. 54 - 5512-28 evens,32-36 evens