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In mathematics, numbers are classified according to common characteristics. Every number is classified as belonging to one or more of the following sets.

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Presentation on theme: "In mathematics, numbers are classified according to common characteristics. Every number is classified as belonging to one or more of the following sets."— Presentation transcript:

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2 In mathematics, numbers are classified according to common characteristics. Every number is classified as belonging to one or more of the following sets of numbers: Natural Numbers: Whole Numbers: Integers: Rational Numbers: Irrational Numbers: Real Numbers: Imaginary Numbers: Complex Numbers: Classifying Numbers

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5 For a repeating or periodic decimal, the digits in the quotient follow a recurring pattern. The digits that repeat are called the. The number of digits repeating is called the of the period. Rational Numbers - Repeating Decimals

6 Expressing Rational Numbers in the form Example: Express 0.4 as a fraction in lowest terms. Following the rule of 9’s: 1. All digits to the right of the decimal are repeating. 2. The digits repeating (or the period) form the numerator. 3. The length determines the number of 9s in the denominator.

7 Solve algebraically: Express 0.4 in the form 1. Assign a variable to form an equation. 2. Multiply both sides of the equation by a power of 10 equivalent to the number of digits repeating. 3. Subtract the two equations. 4. Solve for n.

8 Express 0.83 in the form 1. Assign a variable to form an equation. 2. Multiply both sides of the equation by a power of 10 to move any non-repeating digits to the left of the decimal. 3. Multiply both sides of the equation by a power of 10 equivalent to the number of digits repeating. 4. Subtract the two equations. 5. Solve for n. Solve algebraically:

9 A shortcut for expressing 0.83 in the form To find the numerator: subtract any digits that are not repeating from the digits to the right of the decimal. To find the denominator: for any digits repeating include that many 9s. for any digits not repeating, add zeros in the denominator. Therefore, the denominator is Therefore the numerator is.

10 Absolute Value Absolute value is the distance from zero on the real number line. Evaluate: | -8 | = | | = | | = | | - | | =

11 Page 20-22: 1aceg, 3, 4, 5acegi, 6ab, 7bc, 8bc, 9, 10, 12 Page 27 – 31: 2abef, 4, 6, 7, 9a, 10, 11bcfg, 19


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