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Real Numbers and Number Lines

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Whole Numbers whole numbers natural numbers This figure shows a set of whole numbers. The whole numbers include 0 and the natural, or counting, numbers. The arrow to the right indicates that the whole numbers continue indefinitely. Zero is the least whole number. 123456789101112130

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Integers integers A number line can be used to represent a set of integers. Integers include 0, the positive integers, and the negative integers. The arrows indicate that the numbers go on forever in both directions. 1234560-2-3-4-5-6 negative integerspositive integers

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Rational Numbers rational numbers A number line can also show rational numbers. A rational number is any number that can be written as a fraction, a/b, where a and b are integers and b cannot equal 0. There are infinitely many rational numbers between two integers. Rational numbers can also be represented by decimals. 3/8 = 0.375 2/3 = 0.666...0/5 = 0

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terminatingnonterminating Decimals may be terminating or nonterminating. 0.375 and 0.49 are terminating decimals. 0.666... and -0.12345... are nonterminating decimals. Some nonterminating decimals have a repeating pattern. 0.171717... repeats the digits 1 and 7 to the right of the decimal point. Each rational number can be expressed as a terminating decimal or a nonterminating decimal with a repeating pattern.

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When a number(s) has a line over the top of it, like 0.17, it is read as zero point one seven repeating.

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Irrational Numbers irrational numbers Decimals that are nonterminating and do not repeat are called irrational numbers. 6.028716... and 0.101001000... appear to be irrational numbers

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Real Numbers Real numbers Real numbers include both rational and irrational numbers.

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coordinate origin The number that corresponds to a point on a number line is called the coordinate of the point. Coordinate 0 is called the origin. 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. measure AB

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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 AB measure = a - b

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absolute value One way to calculate the measurement of a distance is by using absolute value. The absolute value of a number is the number of units a number is from zero on the number line. In symbols, the absolute value is denoted by two vertical slashes.

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Real Numbers Irrational Numbers Integers Rational Numbers Whole Numbers Natural Numbers -5/2 2/3 0.65 0.9 -5-7 0 3 1 2 0.12122... 0.010011...

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All information taken from the Glencoe Geometry – Concepts and Applications, pg. 50-54.

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