7.9 Negative Exponents and 7.10 Scientific Notation bn Remember the rule m b n m ? b What happened if m > n? What happened if m = n? 1. So to review…. a 2 b 3 a 5 a 2 (3x 2 )1 = 2 x 2 ( x) = 2. Population of a certain state in x years from now can be estimated from the formula P 12(1.03) x million. Estimate (in millions) what the population will be…. (a) now (b) 10 years from now (c) 10 years ago 3. The cost of living in a certain city has been increasing so that an item costing one dollar today may cost (1.08) x dollars in x years. How much may it cost in 3 years? How about 9 years? How about 9 years ago? 7.10 Scientific Notation When some numbers are so large, or so small that it becomes too difficult to read them or perhaps more importantly to write them, we can use scientific notation to simplify the expression. When using scientific notation, we always want to write a real number that is greater than or equal to 1 and less than 10 and multiply that number by 10 to an integral power. 200 = 2 x 100 = 2 x 10 2 .003 = 3 3 x 10 3 1000 1. What does 18,000 look like in scientific notation? (a) 18 x 103 (b) 1.8 x 103 (c) 1.8 x 10 4 (d) 2 x 10 4 2. 3,600,000 mi² (area of the U.S. ) = 3. .000000001 seconds (a nanosecond) = 4. 1,390,000,000 km (diameter of the sun) = 5. Diameter of the sun in meters = 6. Go back and answer question number 2 on the previous page using scientific notation. 7a. If light travels at 270,000 km/sec. How far does it travel in one year (use 365 days in a year)? This by definition, is a light year. 7b. Andromeda galaxy is 1.5 x 106 light years away from Earth, find the distance in km. 7c. How long does the light from the sun take to reach Earth? The sun is 1.5 x 108 km from Earth. 7d. Distance from Earth to Alpha Centauri is 4.07 x 1013 km. How long does the light from that star take to reach Earth?