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Scientific Notation why it’s used, when to use it, review of standard sci. notation Why sci. not.? The #s for scien. msmnts are often very large or very small Earth to the Moon is 384,403,000 m E. coli, is .0000011 to .0000015 m wide Standard Scientific Notation Which one is in std. sci.not.? 0.486 x 10-3 km 2.50 x 101 ºC 904.6 x 10-2 g Std. sci.not.: a number between 1 to 9, followed by a decimal point and more digits, then “ x 10 to a power” Power can be negative or positive +/- powers, and moving the decimal Expanding: Putting in std. sci.not: How to use “EE” notation in your calculator and practice problems Scientific Notation Well now what, how do I do all the operations? Addition and Subtraction • Change the #s so that all exp. are the same. • Add or subtract coefficients • Put in std. sci.not. (2.0 x 103) + (3.0 x 102) = (2.0 x 103) + (0.3 x 103) = (2.0 + 0.3) x 103 = 2.3 x 103 Now you try it! (2.35 x 107 g) – (6.32 x 105 g) (4.80 x 108 g) – (1.3 x 103 g) Multiplication • Add the exponents on the 10s together • Multiply the coefficients • Put it together, and put answer in std. sci. not. (4.0 x 105) x (3.0 x 10-1) 105 x 10-1 = 10(5-1) = 104 ( 4.0 x 3.0) x 104 = 12 x 104 1.2 x 103 Now you try! (8.0 x 108 cm) x (6.0 x 102 cm) = (4.78 x 105 cm) x (8.9 x 107 cm) = Division • Divide the coefficients first, put result in numerator • Move power of ten in denominator to numerator, switching the sign on the exponent. It’s now a multiplication problem. • Add the exponents • Put it together and put in std. sci. not. 6.0 x 108 = 2.0 x 108 = 2.0 x 108 x 10-5 = 2.0 x 103 3.0 x 105 1.0 x 105 2.0 x 103 Now you try it! (3.6 x 108 g) = (1.2 x 104 mL) (1.02 x 103 g) = (3.60 x 107 mL) Sci. Not. HW