WARM-UP Write in Scientific Form Write in Standard Form 1) 28,000 5) 4.9× 10 −5 2) 0.078 6) 8.75× 10 6 3) 0.00922 7) 7.433× 10 −4 4) 276,000,000 8) 3.1× 10 2

Module 1 Lesson 7 Operations with Scientific Notation Addition and Subtraction

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.

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 8.28 10 or something like that This is the same as, 8.28× 10 10

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 + 5× 10 6 4+5 × 10 6 9× 10 6

Operation: Adding & Subtracting Note-Taking Guide 9.3× 10 6 − 8.12× 10 6 9.3−8.12 × 10 6 1.18× 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

Operation: Adding & Subtracting Note-Taking Guide 5× 10 5 + 6.23× 10 4

Do these in your notebook! IF TIME 1 2.1 × 10 7 +(6 × 10 7 ) 6.3× 10 4 − 4.25× 10 4 9× 10 3 −(8.1× 10 2 ) 3.25× 10 −2 + 4.75× 10 −4 2 3 4

Module 1 Lesson 8 Operations with Scientific Notation Multiplication and Division

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.

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

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

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

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

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 ) 9.6 1.6 × 10 7−4 6× 10 3 Could we do something similar to solve this problem? (9.6× 10 7 ) (1.6× 10 4 )

Operation: Division Note-Taking Guide 4.5× 10 −5 1.6× 10 −2 4.5 1.6 × 10 −5−(−2) 2.8125× 10 −3 7.2× 10 −9 1.2× 10 2 7.2 1.2 × 10 (−9)−2 6× 10 −11

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

Do these in your notebook! IF TIME (9.1× 10 7 ) (6× 10 5 ) 6.3× 10 −2 4.25× 10 4 9× 10 3 (8.1× 10 3 ) 3.25× 10 −2 (4.75× 10 −4 ) 1 2 3 4