Multiplying and Dividing in Scientific Notation

1
Multiplying and Dividing in Scientific Notation

• A.Oman
• Ellerbruch.Nmu.Edu

2
Multiplying Numbers in Scientific Notation

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

3
Example 1

• Given (3.42 X 105)(4.67 X 109)
• Multiply bases 3.42 X 4.67 15.97
• Add Exponents 10510910591014
• Answer 15.97 X 1014
• Shift Decimal left one place.
• Final Answer 1.597 X 1014

4
Example 2

• Given (2.93 X 10-2)(8.3 X 10-5)
• Multiply Bases 2.93 X 8.3 24.319
• Add Exponents 10-210-510-2(-5)10-7
• Answer 24.319 X 10-7
• Shift decimal left one place.
• Final Answer 2.43 X 10-6

5
Practice Worksheet

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

6
Dividing Numbers in Scientific Notation

• Divide the base numbers.
• Then subtract the exponents to get the power of
  10.
• General formula
• N X 10x / M X 10y N/M X 10x-y

7
Example 1

• Given8 X 10-3 / 2 X 10-2
• Divide bases 8/24
• Subtract exponents (-3)-(-2)-1
• Answer 4 X 10-1

8
Example 2

• Given3.45 X 102 / 1.23 X 10-5
• Divide bases 3.45/1.23 2.81
• Subtract exponents (2)-(-5)7
• Answer 2.81 X 107

9
Practice Worksheet

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

10
Links for more information and practice

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