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Multiply Numbers Written in Scientific Notation

Multiply Numbers Written in Scientific Notation. 8 th Grade Math September 4, 2013 Ms. DeFreese. On-line Lesson and Practice. http://learnzillion.com/lessons/1293-multiply-numbers-in-scientific- notation http://www.ixl.com/math/grade-8/multiply-numbers-written-in-scientific- notation.

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Multiply Numbers Written in Scientific Notation

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  1. Multiply NumbersWritten in Scientific Notation 8th Grade Math September 4, 2013 Ms. DeFreese

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

  3. Assignment: multiply the following and put your answer in Scientific Notation • 1. (8 x 104)(3 x 102) • 2. (7 x 10-2)(8 x 10-4) • 3. (4 x 105)(2 x 10-5) • 4. (1.5 x 107)(3 x 1012) • 5. (1.2 x 10-8)(2 x 10-3) • 6. (8 x 101)(8 x 105) • 7. (3.4 x 105)(1 x 102) • 8. (4 x 10-7)( 4 x 105) • 9. (6 x 105)(6 x 10-7) • 10. (3 x 10-5)(2 x 1012)

  4. 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 :

  5. 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 1011 the number 11 is referred to as the exponent or power of ten.

  6. Rules for Multiplication in Scientific Notation • 1) Multiply the coefficients • 2) Add the exponents (base 10 remains) Example 1: (3 x 104)(2x 105) = 6 x 109

  7. What happens if the coefficient is more than 10 when using scientific notation? • Example 2: (5 x 10 3) (6x 103) = 30. x 106 • 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.x106 = 3.0 x 107in scientific notation.

  8. 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 104)(5 x 106)(3 x 102) = 105. x 10 12= 1.05 x 10 14

  9. (2 X 103)(4X104)= • 8 x 107 • (6 X 105 )(7 X 10 6)= • 42 x 1011 = 4.2 x 1012 • (5.5 X 107)(4.2 x 104)= • 33.1 x 1011 = 3.31 x 1012

  10. 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 108) = 6. x 105

  11. (3 X 10-6)(2X10-4)= • 6 x 10-12 • (5 X 10-5 )(7 X 10 10)= • 35 x 105 = 3.5 x 106 • (5.5 X 10-7)(4.2 x 104)= • 33.1 x 10-3 = 3.31 x 10-2 • (5 X 107)(8 x 10-6)(4.2 x 104)= • 168.2 x 105 = 1.682 x 107

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