lesson 2-1 real numbers and number lines. ohio content standards:
TRANSCRIPT
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Lesson 2-1Lesson 2-1Real Numbers and Number
Lines
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Ohio Content Standards:
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Ohio Content Standards:• Apply properties of operations and the
real number system, and justify when they hold for a set of numbers.
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Whole Numbers
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Whole Numbers
• Includes zero and the Natural Numbers
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Whole Numbers
• Includes zero and the Natural Numbers
• Natural Numbers are also called the Counting Numbers
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Integers
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Integers
• Includes zero, the positive integers, and the negative integers
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Rational Numbers
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Rational Numbers
• Any number that can be written as a fraction
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Rational Numbers
• Any number that can be written as a fraction
• Terminating Decimals are rational
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Rational Numbers
• Any number that can be written as a fraction
• Terminating Decimals are rational
• Repeating Decimals are rational
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Irrational Numbers
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Irrational Numbers
• Decimals that are nonterminating and do not repeat
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Real Numbers
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Real Numbers
• Include both rational and irrational numbers
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Postulate 2-1Number Line Postulate
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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.
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For each situation, write a real number with ten digits to the right of the
decimal point.
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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
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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
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Coordinate
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Coordinate
• Number that corresponds to a point on a number line
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Origin
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Origin
• Has coordinate zero
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Postulate 2-2Distance Postulate
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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.
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Postulate 2-3 Ruler Postulate
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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.
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Absolute Value
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Absolute Value
• Number of units a number is from zero on the number line.
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Absolute Value
• Number of units a number is from zero on the number line.
• Symbol : two vertical slashes
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Use the number line to find CE.
-3 -2 -1 0 1 2 3
A GFEDCB
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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?
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Assignment:
Pgs. 54 - 5512-28 evens,32-36 evens