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10/27/2009 Definition Scientific Notation Objectives: To express numbers using scientific notation and to convert numbers to and from scientific notation. Example: 3.56 x 102 Example: 2 2.893 893 x 10-6 Scientific notation is used to represent very large or very small numbers. Examples: Write each number using scientific notation. Steps Move the decimal so that the number is between 0 and 10. To make the this number equal to the original: Count the number of places you would move the decimal. This will be the exponent on ten. If decimal was moved to right, power of ten is positive. If decimal was moved to left, power of ten is negative. For negative number, follow same steps using absolute value. Then make answer negative. a) 63,000 b) 5,870,000 c) 0.56389 d) -12.652 e) -0.00054 Examples – Write without exponents. SOLUTIONS a) 63,000 b) 5,870,000 c) 0.56389 d) -1265.2 e) -0.00054 Scientific notation: a number between 0 and 10 times a power of 10 6.3 x 104 5.87 x 106 5.6389 x 10-1 -1.2652 x 103 -5.4 x 10-4 f) g) h) i) 4.56 x 103 -1.225 x 10-2 0.372 x 105 7.862356 8623 6 x 107 1 10/27/2009 SOLUTIONS f) g) h) i) 4.56 x 103 -1.225 x 10-2 3.372 x 105 7.862356 x 107 f) g) h) i) 4,560 -0.01225 337,200 78,623,560 2