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APPENDIX II "Manipulating Numbers in Scientific Notation" Answers Practice: 1. Write the following numbers in scientific notation; keep only 3 significant figures. a) b) c) d) e) 9,876,543 1,000 1,000,000,000 0.000009876543 0.000000001000 9.88 x 106 1.00 x 103 1.00 x 109 9.88 x 10–6 1.00 x 10–9 2. Multiply and divide the following numbers. a) 108 times 10-3 108+(–3) = 105 b) 108 divided by 10-3 108–(–3) = 1011 c) 14 x 1015 times 2 x 10-12 (14 x 2) x 1015+(–12) = 28 x 103 = 2.8 x 104 d) 14 x 1015 divided by 2 x 10-12 (14 ൊ 2) x 1015–(–12) = 7 x 1027 e) (9 x 109)(1.6 x 10-19)(1.6 x 10-19) divided by (5 x 10-5) (9 x 1.6 x 1.6 ൊ 5) x 109+(–19)+(–19)–(–5) = 4.608 x 10–24 Ciardi, T Scientific Notation 1 3. A wavelength of blue light is 450 nanometers or 450 x 10–9 meters. What is this wavelength in standard notation? 450 x 10–9 Since this is a negative exponent, we need to move the decimal to the left, nine places. 450 x 10–9 = 0.000000450 4. Our sister galaxy, the Andromeda galaxy is 250 Million light years, or 250 x 106 light years from us, and 1 light year is 9.46 x 1015 meters. If we multiply the two numbers together, the number of light years times the number of meters in a light year, we can know the total distance in meters. Write the total distance in meters to the Andromeda Galaxy, in standard notation. First, multiply the numbers (250 x 106 LY) x (9.46 x 1015 meters/LY) = 2.3 x 1024 meters Now we can write the answer in standard notation. Since this is a positive exponent, we need to move the decimal to the right, 24 places. 2,300,000,000,000,000,000,000,000 meters (This is why we use scientific notation) This is 1,469,900,000,000,000,000,000 miles! Ciardi, T Scientific Notation 2