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44 * 101. 2 Exponents and Scientiﬁc Notation b. 8 104 = a b * ¢ -2 ≤ -2 3 3 * 10 10 31 Regroup factors. 6 * 104 - (-2) Subtract the exponents on 10 and divide the other parts. 6 * 106 = (6 * 10-1) * 106 Simplify: 4 - (-2) = 4 + 2 = 6. 6 = 6 * 10-1. ● ● ● Check Point 11 Perform the indicated computations, writing the answers in scientiﬁc notation: a. 1 * 105)(5 * 10-7) b. 2 * 106 . 3 * 10-3 Applications: Putting Numbers in Perspective Due to tax cuts and spending increases, the United States began accumulating large deﬁcits in the 1980s.

2 trillion. 2 * 1012 dollars. S. 12 * 108. If the national debt was evenly divided among every individual in the United States, how much would each citizen have to pay? 12 * 108. S. citizen would have to pay approximately $48,700 to the federal government to pay off the national debt. 6 trillion for the wars in Iraq and Afghanistan. S. 12 * 108). If the cost of these wars was evenly divided among every individual in the United States, how much, to the nearest hundred dollars, would each citizen have to pay?

The absolute value of a positive number is the number itself. Thus, 0 23 - 1 0 = 23 - 1. b. 14, the number inside the absolute value bars, 2 - p, is negative. The absolute value of x when x 6 0 is -x. Thus, ͉ 2 - p͉ = -(2 - p) = p - 2. c. If x 6 0, then |x| = -x. Thus, ͉ x͉ -x = = -1. x x ● ● ● Check Point 6 Rewrite each expression without absolute value bars: a. 0 1 - 22 0 b. ͉ p - 3͉ c. ͉ x͉ if x 7 0. 1 Algebraic Expressions, Mathematical Models, and Real Numbers DISCOVERY Verify the triangle inequality if a = 4 and b = 5.

### College Algebra Essentials by Robert F. Blitzer

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