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Absolute Value Find the absolute value of a number Just how far from zero are you?

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Absolute Value Absolute value of a number is the DISTANCE to ZERO.Absolute value of a number is the DISTANCE to ZERO. Remember distance itself is ALWAYS positive -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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Be careful! In math a negative sign in front of the absolute value sign should be read “take the opposite of”. This means treat the absolute value sign like a grouping symbol. Do the work inside first THEN take the opposite of

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Opposites Two numbers that have the same ABSOLUTE VALUE, but different signs are called opposite pairs. (Zero Pairs) Example -6 and 6 are opposite pairs (Zero Pairs) because both are 6 units away from zero. | -6 | = 6 and | 6 | = 6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.

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Rational Numbers Real numbers consist of all the rational and irrational numbers. The real number system has many subsets: –Natural Numbers –Whole Numbers –Integers

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Natural Numbers Natural numbers are the set of counting numbers. {1, 2, 3,…}

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Whole Numbers Whole numbers are the set of numbers that include 0 plus the set of natural numbers. {0, 1, 2, 3, 4, 5,…}

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Integers Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…}

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Rational Numbers Rational numbers are any numbers that can be expressed in the form of, where a and b are integers, and b ≠ 0. They can always be expressed by using terminating decimals or repeating decimals.

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Terminating Decimals Terminating decimals are decimals that contain a finite number of digits. Examples: 36.8 0.125 4.5

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Repeating Decimals Repeating decimals are decimals that contain a infinite number of digits. Examples: 0.333… 7.689689… FYI…The line above the decimals indicate that number repeats.

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Venn Diagram of the Real Number System Rational Numbers

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To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. Rational Numbers Integers Whole Numbers Natural Numbers 117 0 6.36 -3

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Solution Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number: –117 is a natural number, a whole number, an integer, and a rational number. – is a rational number. –0 is a whole number, an integer, and a rational number. –-3 is an integer and a rational number. –6.36 is a rational number. – is an irrational number.

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