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Lesson 2-1 Real Numbers and Number Lines

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Ohio Content Standards:

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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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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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Includes zero, the positive integers, and the negative integers

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Rational Numbers

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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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Decimals that are nonterminating and do not repeat

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Real Numbers

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Include both rational and irrational numbers

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Postulate 2-1 Number Line Postulate

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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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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

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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 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

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Coordinate

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Number that corresponds to a point on a number line

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Origin

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Has coordinate zero

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Postulate 2-2 Distance Postulate

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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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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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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 AGFEDCB

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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 evens, evens

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