j. Express and use numbers in scientific notation. .

1. M8N1 Students will understand different representations of numbers including square roots, exponents, and scientific notation. j. Express and use numbers in scientific notation. . K. Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation

2. ESSENTIAL QUESTIONS • When is the decimal negative or positive? • What the exponent means in scientific notation? • How do we multiply a whole number by a power of 10? • How do we multiply a decimal by a power of 10? • How do we divide a whole number by a power of 10? • How do we divide a decimal by a power of 10?

3. SPONGE: Aug.31 Can You Find The Pattern? 2^4 = 16 2^3 = 8 2^2 = 4 2^1 = 2 2^0 = 1 What is the next exponent for 2 ? What is the next value in the pattern?

4. Writing very LARGE and SMALL Numbers Scientific Notation: number written to show one digit to the left of the decimal point, two digits to the right of the decimal point, and includes a base 10 with an exponent.

5. VocabularyKLW Chart • Scientific notation • Exponent/exponential form • Standard form • Base ten • Pattern • Negative Exponent • Exponent of Zero

6. MULTIPLYING AND DIVIDING BY POWERS OF 10 How do we multiply a whole number by a power of 10? Examples: Add on as many 0's as appear in the power. 36 × 10  = 360   Add on one 0. To divide a whole number by a power of 10. 265,000 ÷ 100 = 2,650 cancel out two zeroes

7. Multiply a Decimal How do we multiply a decimal by a power of 10?  7.32 × 10    Move the decimal point right as many digits as there are zeros in the power. 7.32 × 10 = 73.2 7.32 × 100 = 732     7.32 × 1000 = 7,320

8. Working Together X = X = What patterns do you see in your answers?

9. Work Period As a group, complete The Power of 10 and discuss the questions below. One person from the group will explain your reasonable response. Strategy: THINK-PAIR-SHARE

10. CLOSING Aug 31 STUDENT PRESENTATIONS AND ADD TO K-W-L HOMEWORK: GROWING, GROWING, GROWING INVESTIGATION 5, PAGE 70, NUMBERS 55-56

11. Sponge Sept 1 In your own words, explain how to write these numbers in SN. a). 634,930 b). 0.0000407

12. How many sunflowers are in this field? M8N1 Students will understand different representations of numbers including square roots, exponents, and scientific notation. j. Express and use numbers in scientific notation. . K. Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation

13. Divide a Decimal How do we divide a decimal by a power of 10?  63.4 ÷ 10   Move the decimal point left as many digits as there are 0's in the power. If there are not enough digits, add on 0's.

14. Examples 63.4 ÷ 10 =6.34 63.4 ÷ 100=.634   63.4 ÷ 1000=.0634   Finally, to divide a whole number by a power of 10. 265,000 ÷ 100 = 2,650

15. Work Together

16. WORK PERIOD Sept 1 Performance Task: Exploring the Power of Ten

17. Closing Sept.1 Explain how to write each of the following in standard form. 1.23 x 10^-3 1.23 x 10^3 1.23 x 10^-6 1.23 x10^0 HOMEWORK: Worksheet Scientific Notation

18. How much water do the people of Atlanta use daily? 9, 100, 000, 000 liters

19. What is the mass of the sun? 2 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000g So how to write this in a simpler way??

20. Scientific Notation: is used to make very LARGE or very SMALL numbers easier to handle.

21. RULE 1: SN only replaces zeroes! These zeroes represent decimal places! EXAMPLE: 45,000,000,000,000,000= 4.5 x 10^16 decimal places after the 4 to the end of the number!

22. RULE 2: There is only one number in front of the decimal. EXAMPLE: 4. 1349494 x 10^-9 Just remember that every number will be less than 10!

23. RULE 3: When moving the decimal RIGHT, the exponent will be negative EXAMPLE: 0.0000432 = 4.32 x 10^-5 SMALL NUMBERS will always have a negative exponent.

24. RULE 4: When moving the decimal LEFT, the exponent will be POSITIVE! 55, 000, 000, 000 = 5.5 x 10^10 LARGE NUMBERS will always have a positive exponent