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Simplify the following Write all the answers using positive exponents. 1) 4 0 = 1 4) = – 72) – 7w 0 3) 5)

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15.05 Scientific Notation

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Scientific Notation is used to write very large and very small numbers. Numbers like: Scientific Notation Form where a > 1 and a < 10 and n is an integer 93,000,0000.000025

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Scientific Notation Form a × 10 n To write an number in scientific notation form, move the decimal point until a number between 1 and 10 is reach. This is the “a” value. To find the “n” value. Count the number of decimal places moved. “n” is positive if the decimal was moved to the left. “n” is negative if the decimal was moved to the right.

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Scientific Notation Form S.N. a × 10 n Write the following numbers in S.N. 93,000,000 There’s no decimal point, place one at the end. 93,000,000.0 Move the decimal point between the 9 and 3 and count the number of decimal places moved. 9.3 × 10 7 0.000025 Move the decimal point between the 2 and 5 and count the number of decimal places moved. 2.5 × 10 – 5

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To write a S.N. number without the exponents, move the decimal point “n” places. = 186,000 Move the decimal 5 places to the right. 1.86 × 10 5 = 0.00000082 Move the decimal 7 places to the left. 8.2 × 10 – 7 Move the decimal to the left if “n” is negative. Move the decimal to the right if “n” is positive. 4 × 10 3 = 4,000 9 × 10 – 5 = 0.00009

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To find the product or quotient of numbers written in S.N., find the product or quotient of the “ a ” terms and of the “ 10 n “ terms. ( 2 × 10 3 )( 3 × 10 5 ) ( 8 × 10 – 2 )( 4 × 10 9 ) = 3.2 × 10 8 = ( 2 · 3 ) × ( 10 3 · 10 5 ) = 6 × 10 8 = ( 8 · 4 ) × ( 10 – 2 · 10 9 ) = 32 × 10 7 6 × 10 8 2 × 10 3 _______ 2 610 8 10 3 = ___ × ____ = 3 × 10 5 ________ 2 × 10 2 5 × 10 – 7 = ___ 2 5 × ____ 10 2 10 – 7 = 0.4 × 10 9 = 4 × 10 10

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Try This: ( 3 × 10 2 )( 6 × 10 – 8 ) 8 × 10 – 5 = 0.00008 = 18 × 10 – 6 ________ 9 × 10 7 2 × 10 6 = 4.5 × 10 1 Write the following in Scientific Notation 25000= 2.5 × 10 4 Write the following without Scientific Notation Simplify = 1.8 × 10 – 5

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Objective The student will be able to: express numbers in scientific and decimal notation.

Objective The student will be able to: express numbers in scientific and decimal notation.

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