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Multiply Numbers Written in Scientific Notation 8 th Grade Math September 4, 2013 Ms. DeFreese

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On-line Lesson and Practice http://learnzillion.com/lessons/1293-multiply- numbers-in-scientific-notation http://learnzillion.com/lessons/1293-multiply- numbers-in-scientific-notation http://www.ixl.com/math/grade-8/multiply- numbers-written-in-scientific-notation http://www.ixl.com/math/grade-8/multiply- numbers-written-in-scientific-notation

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Assignment: multiply the following and put your answer in Scientific Notation 1. (8 x 10 4 )(3 x 10 2 ) 2. (7 x 10 -2 )(8 x 10 -4 ) 3. (4 x 10 5 )(2 x 10 -5 ) 4. (1.5 x 10 7 )(3 x 10 12 ) 5. (1.2 x 10 -8 )(2 x 10 -3 ) 6. (8 x 10 1 )(8 x 10 5 ) 7. (3.4 x 10 5 )(1 x 10 2 ) 8. (4 x 10 -7 )( 4 x 10 5 ) 9. (6 x 10 5 )(6 x 10 -7 ) 10. (3 x 10 -5 )(2 x 10 12 )

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More Notes: Scientific Notation is based on powers of the base number 10. The number 123,000,000,000 in scientific notation is written as :

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The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10 11 the number 11 is referred to as the exponent or power of ten.

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Rules for Multiplication in Scientific Notation 1) Multiply the coefficients 2) Add the exponents (base 10 remains) Example 1: (3 x 10 4 )(2x 10 5 ) = 6 x 10 9

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What happens if the coefficient is more than 10 when using scientific notation? Example 2: (5 x 10 3 ) (6x 10 3 ) = 30. x 10 6 While the value is correct it is not correctly written in scientific notation, since the coefficient is not between 1 and 10. We then must move the decimal point over to the left until the coefficient is between 1 and 10. For each place we move the decimal over the exponent will be raised 1 power of ten. 30.x10 6 = 3.0 x 10 7 in scientific notation.

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Example 3: (2.2 x 10 4 )(7.1x 10 5 ) = 15.62 x 10 9 = 1.562 x 10 10 Example 4: (7 x 10 4 )(5 x 10 6 )(3 x 10 2 ) = 105. x 10 12 = 1.05 x 10 14

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(2 X 10 3 )(4X10 4 )= 8 x 10 7 (6 X 10 5 )(7 X 10 6 )= 42 x 10 11 = 4.2 x 10 12 (5.5 X 10 7 )(4.2 x 10 4 )= 33.1 x 10 11 = 3.31 x 10 12

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What happens when the exponent(s) are negative? We still add the exponents. Example 5: (3 x 10 -3 ) (3x 10 -3 ) = 9. x 10 -6 Example 6: (2 x 10 -3 ) (3x 10 8 ) = 6. x 10 5

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(3 X 10 -6 )(2X10 -4 )= 6 x 10 -12 (5 X 10 -5 )(7 X 10 10 )= 35 x 10 5 = 3.5 x 10 6 (5.5 X 10 -7 )(4.2 x 10 4 )= 33.1 x 10 -3 = 3.31 x 10 -2 (5 X 10 7 )(8 x 10 -6 )(4.2 x 10 4 )= 168.2 x 10 5 = 1.682 x 10 7

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