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§ 4.3 Scientific Notation

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Angel, Elementary Algebra, 7ed 2 Scientific Notation A number written in scientific notation is written as a number greater than or equal to 1 and less than 10 (1 a 10) multiplied by some power of 10. The exponent on the 10 must be an integer. Example: a.) 1.5 x 10 4 b.) 7.03 x 10 -2

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Angel, Elementary Algebra, 7ed 3 Writing in Scientific Notation 1.Move the decimal point to the right of the first nonzero digit. This will give a number greater than or equal to 1 and less than 10. 11,543 1.1543 2.Count the number of places you moved the decimal point to obtain the number in step 1. If the original number was 10 or greater, the count is positive. If the original number was less then 1, the count is negative. 1.1543 4 places

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Angel, Elementary Algebra, 7ed 4 Writing in Scientific Notation 3.Multiply the number obtained in step 1 by 10 raised to the count (power) found in step 2. 1.1543 10 4 4 places 11,543 = 1.1543 x 10 4 Example : a.) 0.000723 = 7.23 x 10 -4 b.) 541,000 = 5.41 x 10 5

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Angel, Elementary Algebra, 7ed 5 Converting from Scientific Notation 1.Observe the exponent of the power of 10. 3.8 x 10 4 Exponent is +4 2.a) If the exponent is positive, move the decimal point in the number to the right the same number of places as the exponent. (This will result in a number greater than or equal to 10.) 4 places 3.8 x 10 4 = 38000 b) If the exponent is negative, move the decimal point in the number to the left the same number of places as the exponent. (This will result in a number less than 1.) 3.8 x 10 -4 = 0.00038 4 places

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Angel, Elementary Algebra, 7ed 6 Calculations Using Scientific Notation a.) (2 x 10 -3 )(3 x 10 2 ) = (2 x 3)(10 -3 x 10 2 ) = 6 x 10 -1 = 0.6 b.)

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