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1. Scientific Notation is used due to the large and small numbers used by scientists. For example the nearest star to our solar system is 41 500 000 000 000 000 000 mm. We do not write this number this way but use scientific notation to shorten the way the number is written which is 4.15 x 1019mm In this notation a number has the form M x 10n Where the M is a number and n is called index or exponent and is a positive or negative number. To change a number into scientific notation a) Determine the number M by moving the decimal point so that you leave only one non zero digit to the left of it. b) M contains all the significant digits indicated by the measurement. (We will discuss this later) c) Determine the index n by counting the number of places you have moved the decimal point. If the decimal is moved to the left n is positive and if moved to the right n is negative. Example #1 Convert to Scientific Notation a) 48000 = 4.8 x 104 b) 7330000 = 7.33 x 106 c) 0.000345 = 3.45 x 10-4 d -0.00000056 = -5.6 x 10-7 e) 3567000 = f) 0.00005677 = g) -678 = h) -0.000000000000345 = Example #2 Convert into an ordinary number a) 5.56 x 104 = 55600 b) 4.78 x 10-6 = 0.00000478 c) -4.67 x 10-4 = -0.000467 d) -3.678 x 109 = -3678000000 e) 4.67 x 10-12 = f) -6.78 x 1015 = g) -8.9 x 107 = h) -561 x 10-15 = Assignment Question #’s 1 and 2 from handout Scientific Notation Operations a) Multiplication and Division using Scientific Notation Recall Laws of Exponents 1. Multiplication Law (xa)(xb) = xa+b 2. Divison Law (xa)÷(xb) = xa-b 3. Power (xa)b = xab Examples on board When multiplying numbers expressed in scientific notation, the exponents of powers of 10 are added even if they are not the same. You multiply the numbers preceding the powers of 10 and then add the exponents to get the product. For example (4.3 x 104)(6.2 x 105) = 26.7 x 109. This value must then be completely simplified to 2.67 x 1010. Additional examples on board. When dividing you follow similar steps as in multiplication except the exponents are subtracted. For example (4.3 x 104)(6.2 x 105) = 0.69 x 10-1 = 6.9 x 10-2 Additional examples on board. Assignment Question # 3 from handout b) Addition and Subtraction When adding or subtracting numbers expressed in scientific notation the values of the exponents must first be converted to similar values and then the numbers preceding the powers of 10 can be added or subtracted. For example 1. 4.3 x 104 + 6.2 x 105 = 0.43 x 105 + 6.2 x 105 = 6.63 x 105 2. 4.3 x 104 – 6.2 x 105 = 0.43 x 105 – 6.2 x 105 = -5.77 x 105 Additional examples on board Assignment Question #’s 4 and 5 from handout