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Published byArlene Bathsheba Watkins Modified over 7 years ago

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**Multiplying and Dividing in Scientific Notation**

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**Multiplying Numbers in Scientific Notation**

Multiply the coefficients together. Then add the exponents to get the power of 10. General formula: (N X 10x) (M X 10y) = (N) (M) X 10x+y

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Moving the Decimal For each move of the decimal to the right you have to add -1 to the exponent. For each move of the decimal to the left you have to add +1 to the exponent.

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Example 1 Given: (3.42 X 105)(4.67 X 109) Multiply coefficients: 3.42 X 4.67 = 15.97 Add Exponents: 105x109=105+9=1014 Answer: X 1014 Shift Decimal left one place. Final Answer: X 1014

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**Example 2 Given: (2.93 X 10-2)(8.3 X 10-5)**

Multiply coefficients: 2.93 X 8.3 = Add Exponents: 10-2x10-5=10-2+(-5)=10-7 Answer: X 10-7 Shift decimal left one place. Final Answer: 2.43 X 10-6

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**Practice Multiplying in Scientific Notation (pdf)**

Practice Worksheet Practice Multiplying in Scientific Notation (pdf) Answers to Worksheet

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**Dividing Numbers in Scientific Notation**

Divide the coefficients. Then subtract the exponents to get the power of 10. General formula: N X 10x / M X 10y = N/M X 10x-y

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**Example 1 Given:8 X 10-3 / 2 X 10-2 Divide coefficients: 8/2=4**

Subtract exponents: (-3)-(-2)=-1 Answer: 4 X 10-1

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Example 2 Given:3.45 X 102 / 1.23 X 10-5 Divide coefficents: 3.45/1.23= 2.81 Subtract exponents: (2)-(-5)=7 Answer: 2.81 X 107

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**Practice Dividing in Scientific Notation (pdf)**

Practice Worksheet Practice Dividing in Scientific Notation (pdf) Answers to Worksheet

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**Links for more information and practice**

Math Skills Multiplying and Dividing with Sci Not (ws 1) Multiplying and Dividing with Sci Not (ws 2)

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