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Scientific Notation What is scientific Notation? Scientific notation is an efficient way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. Why use scientific notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease. Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10x Are the following in scientific notation? Changing standard form to scientific notation. To change standard form to scientific notation… Identify where the decimal point is on the original number Move the decimal point so that the original number becomes a number between 1 and 10. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. Continued… If the original number was less than 1, then the exponent will be negative. If the original number was greater than 1, then the exponent will be positive. Example 1 Given: 289,800,000 Use: 2.898 Decimal place moved 8 places Exponent is 8 Exponent is positive because original number is greater than 1 Answer: 2.898 x 8 10 Example 2 Given: 0.000567 Use: 5.67 Decimal place moved 4 places Exponent is 4 Original number less than 1 so … Exponent is negative Answer: 5.67 x -4 10 Changing scientific notation to standard form. To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent of 10. Move the decimal point to the left for negative exponent 10. Use zeros to fill in places. Example 3 Given: 5.093 x 106 Exponent is positive 6 , move 6 places to make number bigger (to the right). 1 place = 50.93 2 places = 509.3 3 places = 5093. 4 places = 50930. 5 places = 509300. 6 places = 5093000 Answer: 5,093,000 Decimal moved 6 places to the right Example 4 Given: 1.976 x 10-4 Exponent is negative 4, so the number is less than 1. move decimal 4 places to the left to make number less than 1. Answer: 0.0001976 (moved 4 places to the left) Are These in Scientific Notation?? • • • • • • • • • • 23.98393 x 109 4.19385930 x 104 98920.188438 x 10-3 2.22221 x 100 9.002 x 1002 39.992934 x 100 0.1103827493920920284757 x 102 1.00 x 1056 2.39403 x 10-23 9.00078 x 10-1 Even More Practice Below is a list of links to games and activities all having to do with scientific notation. – http://www.aaamath.com/dec71idec2sci.html – http://janus.astro.umd.edu/cgibin/astro/scinote.pl – http://www.sciencejoywagon.com/physicsz one/lesson/00genral/dectosci.htm Now take the quiz to test your scientific notation skills! Click on the link below to take the quiz and then use the answer key for the correct answers. – Quiz – Answers