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TOPIC: Scientific Notation • The number is written as the product of two other numbers: – A number between 1 and 10 (not 10) – and – A power of 10 20.3 x 102 NOT CORRECT 2.03 x 103 CORRECT Converting conventional to scientific notation For numbers 1, the exponent will be positive. Count how many places the decimal is moved. 329 3.29 X 102 Converting conventional to scientific notation For numbers between 0 and 1, the exponent will be negative. Count how many places the decimal is moved. 0.00045 4.5 X 10-4 Converting scientific to conventional notation If the exponent is positive, the number 1, so move the decimal point right. 3.784 X 105 378400 Converting scientific to conventional notation If the exponent is negative, the number is between 0 and 1 so move the decimal point to the left. 2.75 X 10-3 0.00275 Multiplying • • • • (N x 10a) x (M x 10b) = (N x M) x 10a+b (5.1 x 104) x (2.5 x 103) = (5.1 X 2.5) x 10(4+3) (5.1 x 104) x (2.5 x 103) = 12.75 x 107 Oops – new answer isn’t scientific notation – Remember has to be between 1 and 10 – 12.75 = 1.275 – since we made the number smaller we have to make the exponent bigger – 1.275 x 108 Dividing • • • • (N x 10a) / (M x 10b) = (N / M) x 10a-b (3.66 x 10-5) / (2.0 x 10-3) = (3.66/2.0) x 10(-5-(-3)) = 1.83 x 10-5+3 =1.83 x 10-2 • Write this as a normal number .0183 Adding/Subtracting • Exponents must be same number