Multiplying and Dividing in Scientific Notation

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Multiplying and Dividing in Scientific Notation
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Multiplying Numbers in Scientific Notation

• Multiply the decimal numbers together.
• Add the exponents to get the power of 10.
• General formula
• (N X 10x) (M X 10y) (N) (M) X 10xy

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Example 1

• Given 3.42 X 105 4.67 X 109
• Multiply decimals 3.42 X 4.67 15.97
• Add Exponents 105 x 10910591014
• Preliminary Answer 15.97 X 1014
• Now, Rewrite in Scientific Notation if needed.
• Final Answer
• 1.597 X 1015

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Example 2

• Given (2.93 X 10-2) (8.3 X 10-5)
• Multiply Decimals 2.93 X 8.3 24.319
• Add Exponents 10-2 x 10-510-2(-5)10-7
• Answer 24.319 X 10-7
• Rewrite in Scientific Notation
• Final Answer 2.43 X 10-6

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Dividing Numbers in Scientific Notation

• Divide the decimal numbers.
• Then subtract the exponents
• General formula

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Example 1

• Given 8 10-3
• 2 10-2
• Divide decimals 82 4
• Subtract exponents (-3)-(-2) -1
• Final Answer 4 10-1

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Example 2

• Given 3.45 X 102
• 1.23 X 10-5
• Divide decimals 3.45 1.23 2.81
• Subtract exponents 2- -5 7
• Answer 2.81 X 107

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• How to do calculations on your scientific
  calculator
• 1. Make sure that the number in scientific
  notation
• is put into your calculator correctly.
• 2. Read the directions for your particular
  calculator. For basic scientific
  calculators Punch the number (the decimal
  number) into your calculator.
• Push the EE or EXP button. Do NOT use the x
  (times) button!!
• Enter the exponent number. Use the /- button to
  change its sign.
• Voila!
• To check yourself
• multiply 6.0
  x 105 times 4.0 x 103 on your calculator.
• Your answer should be 2.4 x 109.

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Practice Quiz Questions
Question 1 Write these 2 numbers in scientific notation 0.000467 32000000
Question 2 Express 5.43 x 10-3 in standard form
Question 3 (4.5 x 10-14) x (5.2 x 103) ?
Question 4 (6.1 x 105)/(1.2 x 10-3) ?
Question 5 (3.74 x 10-3)4 ?