The document discusses scientific notation, which is used to write very large and small numbers in a standardized way. Scientific notation expresses numbers as the product of a number between 1 and 10 and a power of 10. The document provides examples of writing numbers in scientific notation and standard form. It also discusses patterns in the relationship between the exponent and the place value of the number.

1. Which is greater 5 3 or 3 4 ? 3.54 x 1000 =

2. Which is greater 5 3 or 3 4 ? 3.54 x 1000 = 5 3 = 125 3 4 = 81 3,540

3. 4.8 Scientific Notation

4. Writing Numbers Scientific notation is used to write very large and very small numbers. Today we will focus on only the larger numbers – using positive exponents. The distance to the sun is 150,000,000 km or 1.5x10 8 km.

5. Writing in Scientific Notation In scientific notation, a number is written using “POWERS OF 10’s” Let’s investigate using these powers to understand the pattern.

6. Look for patterns and complete the chart. 1 10 10 10 1 100 1000 10,000 100,000 10x10x10x10x10 10 5

7. What seems to be the relationship between the exponent and the number written in factored form? 1 1 10 0 10 10 10 1 100 10 x 10 10 2 1000 10 x 10 x10 10 3 10,000 10x10x10x10 10 4 100,000 10x10x10x10x10 10 5

8. What seems to be the relationship between the exponent and the number written in decimal form? 1 1 10 0 10 10 10 1 100 10 x 10 10 2 1000 10 x 10 x10 10 3 10,000 10x10x10x10 10 4 100,000 10x10x10x10x10 10 5

9. Scientific Notation Video Exponents and Scientific Notation

10. A number in scientific notation has two parts: A number greater than or equal to 1, but less than 10 multiplied by a power of ten

11. Moving Places 4x10 3 = 4x10x10x10 = 4x1000 = 4000 Notice: the exponent on the 10 is 3 and the decimal after the 4 moved to the right 3 spaces. 2.3x10 5 = 230,000 moving the decimal right 5 spaces. 2.3x10 5 is scientific notation and 230,000 is decimal notation (or standard form).

12. EXAMPLE 1 Writing Numbers in Scientific Notation SOLUTION Exponent is 11 . Move decimal point 11 places to the left. Stars There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation. Standard form 300,000,000,000 Scientific notation 3 10 11 ANSWER The number in scientific notation is 3 x 10 11 .

13. Try these Write each in scientific notation 1) 320,000,000 2) 45,900 3) 20,000,000,000 4) 38 million 38,000,000 5) 9.22 million 9,220,000

14. Try these Write each in scientific notation 1) 320,000,000 2) 45,900 3) 20,000,000,000 4) 38 million 38,000,000 5) 9.22 million 9,220,000 1. 3.2 x 10 8 2. 4.59 x 10 4 3. 2 x 10 10 4. 3.8 x 10 7 5. 9.22 x 10 6

15. Try these Write each in standard form 8.9 x 10 5 5 x 10 4 8.345 x 10 8 2.9 x 10 1 5 x 10 0

16. Try these Write each in standard form 8.9 x 10 5 5 x 10 4 8.345 x 10 8 2.9 x 10 1 5 x 10 0 1. 890,000 2. 50,000 3. 834,500,000 4. 29 5. 5

17. Explain why these example are NOT in scientific notation. Be specific! 38.6 x 10 5 5.2 + 10 8 10 x 10 12 0.4 x 10 6

18. Calculator notation Some calculators show scientific notation the same way we have written them here. Some use EE. They write 3.456 EE5 to mean 3.456 x10 5 . Some write the same thing with this in the screen 3.45605 05 .

19. Homework Page 214 # 1-2, 7-9, 15-16, 20-22