Lesson 2-1 Lesson 2-1 Real Numbers and Number Lines
Dec 15, 2015
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