1. WARM-UP Write in Scientific Form Write in Standard Form
1) 28,000 5) 4.9× 10 −5 2) ) 8.75× ) ) 7.433× 10 −4 4) 276,000,000 8) 3.1× 10 2

2. Module 1 Lesson 7 Operations with Scientific Notation
Addition and Subtraction

3. a  10 n where 1 ≤ a < 10 and n is an integer.
Review
What does scientific notation look like again? Want to see something interesting? Type 3,600,000,000×23 into your scientific calculator… What do you get?
a  10 n where 1 ≤ a < 10 and n is an integer.

4. into your calculator you should see,
Fun Calculator Fact:
When you type 3,600,000,000×23
into your calculator you should see,
8.28 E+10
or something like that
This is the same as,
8.28× 10 10

5. Operation: Adding & Subtracting
Adding and Subtracting numbers written in scientific form have a different rule from multiplying and dividing…
The exponents MUST BE EQUAL!
4× × 10 6
4+5 × 10 6
9× 10 6

6. Operation: Adding & Subtracting
Note-Taking Guide
9.3× 10 6 − 8.12× −8.12 × × 10 6
5.5× 10 −2 + 7× 10 −2
5.5+7 × 10 −2
12.5× 10 −2
But WAIT there’s more…
1.25 x 10-1

7. Operation: Adding & Subtracting
Note-Taking Guide
5× × 10 4

8. Do these in your notebook!
IF TIME 1
2.1 × (6 × ) × − 4.25× 10 4
9× −(8.1× 10 2 ) × 10 − × 10 −4 2 3 4

9. Module 1 Lesson 8 Operations with Scientific Notation
Multiplication and Division

10. Multiplying and dividing numbers written in scientific notation have a different rule from adding and subtracting… To multiply numbers written in scientific notation ______________ the values of “a” and ______________ the exponents.

11. Operation: Multiplication
Note-Taking Guide
How do you think we solve this?
2× ∙ 4× 10 4
Let’s try this…
2× ∙ 4× 10 4
𝟐∙𝟒 × 𝟏𝟎 𝟑+𝟒
8× 10 7

12. Operation: Multiplication
Note-Taking Guide
2.8× × 10 −7
𝟐.𝟖∙𝟓.𝟏 𝟏𝟎 𝟑+(−𝟕)
14.28× 10 −4
WAIT! isn’t between 1 and 10!
1.428× 10 −3

13. Operation: Multiplication
9.1× 10 − × 10 15
𝟗.𝟏∙𝟏.𝟓 𝟏𝟎 −𝟖+𝟏𝟓
13.65× 10 7
WAIT! isn’t between 1 and 10!
1.365× 10 8

14. To divide numbers written in scientific notation ______________ the values of “a” and ______________ the exponents.

15. Could we do something similar to solve this problem?
Operation: Division
Note-Taking Guide
Let’s try this…
(9.6× 10 7 ) (1.6× 10 4 )
× 10 7−4
6× 10 3
Could we do something similar to solve this problem?
(9.6× 10 7 ) (1.6× 10 4 )

16. Operation: Division
Note-Taking Guide
4.5× 10 −5 1.6× 10 − × 10 −5−(−2) × 10 −3
7.2× 10 −9 1.2× × 10 (−9)−2 6× 10 −11

17. Recap: What did we just say?
What is the rule for multiplying numbers written in scientific notation?
𝑎× 10 𝑚 𝑏× 10 𝑛
= (𝑎∙𝑏)× 10 𝑚+𝑛
What is the rule for dividing numbers written in scientific notation?
𝑎× 10 𝑚 𝑏× 10 𝑛
= 𝑎 𝑏 × 10 𝑚−𝑛

18. Do these in your notebook!
IF TIME
(9.1× 10 7 ) (6× 10 5 ) × 10 − × 10 4
9× (8.1× 10 3 ) × 10 −2 (4.75× 10 −4 ) 1 2 3 4