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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 < If n > 0, move the decimal point in a to the right n places x 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 x n = -5 so move the decimal point 5 places to the left n = -5 so move the decimal point 5 places to the left = =

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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

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Observe the number of places n and the direction in which you moved the decimal point the decimal was moved 7 places to the left 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 x x 10 7

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move the decimal to behind the 7. move the decimal to behind the 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 = 7.81 x 10 -4

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