1. Multiplying and Dividing in Scientific Notation

2. 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

3. 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.

4. 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

5. 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

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

7. 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

8. 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

9. 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

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

11. Links for more information and practice
Math Skills
Multiplying and Dividing with Sci Not (ws 1)
Multiplying and Dividing with Sci Not (ws 2)