 # Multiplying and Dividing in Scientific Notation

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Multiplying and Dividing in Scientific Notation

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

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.

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

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

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

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

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

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

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