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Scientific Notation S. Calahan March 2008 Objective: To express numbers in scientific notation and standard form.

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Scientific notation A number in scientific notation is written as A number in scientific notation is written as a x 10 n, where 1 < a < 10 a x 10 n, where 1 < a < 10 and n is an integer. and n is an integer. example: 2.35 x 10 3 example: 2.35 x 10 3

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Scientific to standard form 1. Determine whether n > 0 or n 0 or n < 0. 2. If n > 0, move the decimal point in a to the right n places. 2.45 x 10 8 2.45 x 10 8 n = 8 so move decimal 8 places to the right n = 8 so move decimal 8 places to the right = 245,000,000 = 245,000,000

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If n < 0 Move the decimal point in a to the left n places. Move the decimal point in a to the left n places. 3 x 10 -5 3 x 10 -5 n = -5 so move the decimal point 5 places to the left n = -5 so move the decimal point 5 places to the left = 0.00003 = 0.00003

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Standard to Scientific Notation Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a. Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a. 30,500,000 move the decimal from behind the last zero to behind the three. 30,500,000 move the decimal from behind the last zero to behind the three. 3.0500000 3.0500000

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Observe the number of places n and the direction in which you moved the decimal point. 3.0500000 the decimal was moved 7 places to the left. 3.0500000 the decimal was moved 7 places to the left. n = 7 n = 7 to the left is positive. a = 3.05 a = 3.05 all other zeros are dropped. 3.05 x 10 7 3.05 x 10 7

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0.000781 move the decimal to behind the 7. move the decimal to behind the 7. 0.0007.81 0.0007.81 7.81 7.81 drop the zeros in front of the seven the decimal was moved 4 places to the right. the decimal was moved 4 places to the right. n = -4 a = 7.81 n = -4 a = 7.81 = 7.81 x 10 -4 = 7.81 x 10 -4

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