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Copyright © Swun MathCopyright © Swun Math Grade 8 Unit 3 Lesson 5 C TE

Homework

Unit 3 · Lesson 5: Scientific Notation: Multiply & Divide

(^)
Objective: I will multiply or divide numbers expressed in scientific notation.
Vocabulary Steps
Multiplying in Scientific Notation

1. Multiply coefficients.


2. Add exponents.
   (3 × 102 ) (5 × 104 ) =
   3 × 5 = 15
   10 2+4 = 10^6
   15 × 106
   1.5 × 107
   Proper Scientific Form

Dividing in Scientific Notation^

1. Divide coefficients.


2. Subtract exponents.

(15 × 106 ) ÷ ( 3 × 102 ) =

15 ÷3 = 5

10 6-2 = 10^4

5 × 104

1. Check both numbers are in scientific
   notation.


2. If multiplying-
   
   
   • Multiply coefficients.
   
   
   • Add exponents.
   
   
   
   


3. If dividing-
   
   
   • Divide coefficients.
   
   
   • Subtract exponents.
   
   
   
   


4. Write in scientific notation.

Example # 1 Example # 2

Directions: Simplify the expression. Leave the solution in scientific notation.

(2.5 × 10^3 ) × (8 × 10^2 )

Solution:

• Verify that each number is written in scientific notation.


• Use the commutative property to move your numbers
  around and be able to multiply the two lead numbers
  and the base ten together.


• (2.5 × 8) × (10^3 × 10^2 )


• 20 × 103 + 2


• 20 × 10^5 Not in scientific notation. Need to change 20 to
  2.0


• 2.0 × 10^6
  Answer: 2.0 × 10^6

(9.5 × 10^3 ) ÷ (5 × 10^2 )

Solution:

• Verify that each number is written in scientific notation.


• Change the division problem into a ratio.


• 
  

3

2

9.5 10

5 10

×

×

• Use the commutative property to create two ratios.


• 
  

33

22

9.5 10 9.5 10

5 10 5 10

× →×

×

• Simplify the first ratio by dividing 9.5 by 5.


• 
  

3

2

1.9^10

× 10

Use the rules for multiplying/dividing exponents.

• 1.9 × 103 – 2


• 1.9 × 10^1
  Answer: 1.9 × 10^1

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