1. Scientific Notation Part II Multiplying and Dividing
8th Grade Math
By Mr. Laws

2. Goal/Standards
8.EE.4 – Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation is used.
Interpret scientific notation that has been generated by technology.

3. Essential Question:
Using Math Principle, how can I use the properties of exponents to multiply or divide numbers written in scientific notation?

4. Properties of Exponents
When multiplying or dividing numbers written in scientific notation, when can use the properties of exponents to help get the answer. The following are properties we will use:
Multiplication Property of Exponents
When multiplying bases with exponents, you add the exponents.
Dividing Property of Exponents
When dividing bases with exponents, you subtract the exponents.

5. Multiplying in Scientific Notation Example # 1
Steps
Simplify: (2.5 x 104) (3.4 x 102)
Step 1: x 3.4 = 8.5
Step 1 – Multiply the terminating decimals. (2.5 x 3.4)
Step 2: x 102 = 106
Step 2 – Add the exponents of 104 and 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: x 106

6. Multiplying in Scientific Notation Example # 2
Steps
Simplify: (4.2 x 109) (5.5 x 102)
Step 1: x 5.5 = 23.1
Step 1 – Multiply the terminating decimals. (4.2 x 5.5 )
Step 2: x 102 = 1011
Step 2 – Add the exponents of 109 and 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Is this answer in S.N form? Explain
Step 3: x 1011
Step 4– Change 23.1 to 2.31 by moving decimal point one place to the left, and add 1 exponent to 1011 to make it 1012
Step 4: x 1012

7. Multiplying in Scientific Notation Example # 3
Steps
Simplify: (7.4 x 10-3) (2.5 x 10-3)
Step 1: x 2.5 = 18.5
Step 1 : Multiply the terminating decimals. (7.4 x 2.5 )
Step 2: x 10-3 = 10-6
Step 2 : Add the exponents of 10-3 and 10-3
Step 3 : Rewrite step 1 and step 2 in scientific notation form.
Is this answer in S.N. form? Explain
Step 3: x 10-6
Step 4: Change 18.5 to 1.85 by moving decimal point one place to the left, and add 1 to 10-6 to make it 10-5
Step 4: x 10-5

8. Multiplying in Scientific Notation Practice1. 2. 3. 4.

9. Dividing in Scientific Notation Example # 4
𝟒.𝟐 𝒙 𝟏𝟎 𝟑 𝟐.𝟏 𝒙 𝟏𝟎 𝟏
Steps
Simplify:
Step 1 – Divide the terminating decimals. (4.2 ÷ 2.1)
Step 1: 4.2 ÷ 2.1 = 2
Step 2 – Subtract the exponents of 103 and 101
Step 2: 103 ÷ 101 =102
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: 2 x 102

10. Dividing in Scientific Notation Example # 5
𝟔.𝟗 𝒙 𝟏𝟎 𝟒 𝟐.𝟖𝟒 𝒙 𝟏𝟎 𝟓
Steps
Simplify:
Step 1 – Divide the terminating decimals. (6.9 ÷ 2.84)
Step 1: 6.9 ÷ 2.84 = 2.43
Step 2 – Subtract the exponents of 104 and 105 ( 4 – 5 = -1)
Step 2: 104 ÷ 105 =10-1
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Note: Always check to see if the decimals following the S.N rule.
Step 3: x 10-1

11. Dividing in Scientific Notation Example # 6
𝟓.𝟏 𝒙 𝟏𝟎 −𝟔 𝟔.𝟐 𝒙 𝟏𝟎 𝟓
Steps
Simplify:
Step 1 – Divide the terminating decimals. (5.1 ÷ 6.2)
Step 1: 5.𝟏÷ 6.2 = 0.822
Step 2 – Subtract the exponents of 10-6 and (-6 - 5= -11)
Step 2: ÷ 105 =10-11
Step 3 – Rewrite step 1 and step 2 in scientific notation form.
Step 3: x 10-11
Is this answer in S.N. form? Explain
Step 4: Change to 8.22 by moving decimal point one place to the right, and add -1 exponent to to make it 10-12
Step 4: x 10-12

12. Dividing in Scientific Notation Example # 7
𝟗 𝒙 𝟏𝟎 −𝟒 𝟐.𝟗 𝒙 𝟏𝟎 −𝟔
Steps
Simplify:
Step 1 – Divide the terminating decimals. (9 ÷ 2.9)
Step 1: 9 ÷ 2.9 = 3.103
Step 2 – Subtract the exponents of 10-4 and [-4 – (-6) = = 2]
Step 2: ÷ 10-6 =102
Step 3: x 102
Step 3 – Rewrite step 1 and step 2 in scientific notation form. Check to see if it is in the correct form.

13. Dividing in Scientific Notation Practice1. 2. 3. 4.

14. Summary
What are some important strategies you should remember when multiplying or dividing numbers in scientific notation?
Do you have clear understanding on how to multiply or divide in scientific notation? Explain
Are there any more questions you may have about multiplying and dividing in scientific notation?