1. Warm Up Order each set of numbers from least to greatest. 1. 10, 10, 10, 10 2. 8, 8, 8, 8 3. 2, 2, 2, 2 4. 5.2, 5.2, 5.2, 5.2 04 –1 –2 10, 10, 10, 10 40 –1–2 302 8, 8, 8, 8 320 –2 13 –4 –6 –2 29 –1 5.2, 5.2, 5.2, 5.2 92 –1–2 2, 2, 2, 2 31 –4–6

2. Mathematicians and scientists often work with numbers that are extremely large and numbers that are extremely small.

3. It can be challenging (and boring) to write out such numbers over and over again.

4. Also, a calculator can only fit about 10 digits on its screen.

5. For example, suppose that you were studying the planet Pluto. Pluto is 2,670,000,000 miles away from Earth.

6. 2,670,000,000 is a huge number. Imagine how tedious it would be to write this number multiple times or do calculations with this number.

7. Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these. 2,670,000,000

8. 2,670,000,000 = 2.67 x 10 9 Mathematicians and scientists use a system called scientific notation to abbreviate numbers like these.

9. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power.

10. The exponent tells about the size of the number. A positive exponent means a BIG number. A negative exponent means a small number. Scientific notation has 3 parts. ONLY 1 number in front of the decimal! X multiplication symbol – do not use multiplication dot a power of 10 10 1.25

11. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,000 = 4.5 x 10 7

12. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,000 = 4.5 x 10 7 Notice that there is one digit in front of the decimal point.

13. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,000 = 4.5 x 10 7 The exponent of “7” refers to the number of times that the decimal point “moved.”

14. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,000 = 4.5 x 10 7 The exponent of “7” refers to the number of times that the decimal point “moved.”

15. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,00 0 =4.5 x 10 6 one move

16. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,0 00 =4.5 x 10 5 two moves

17. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000, 000 =4.5 x 10 4 three moves

18. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,00 0,000 =4.5 x 10 3 four moves

19. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,0 00,000 =4.5 x 10 2 five moves

20. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45, 000,000 =4.5 x 10 1 six moves

21. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 4 5,000,000 =4.5 x 10 0 seven moves

22. Scientific notation works by rewriting numbers as the product of a number times 10 to a certain power. 45,000,000 = 4.5 x 10 7 The exponent of “7” refers to the number of times that the decimal point “moved.”

23. Scientific notation can also be used to abbreviate numbers that are really small.

24. .0022 is a really small number that can be rewritten using scientific notation..0022 = 2.2 x 10 -3

25. .0022 is a really small number that can be rewritten using scientific notation..0022 = 2.2 x 10 -3 Notice that there is one digit in front of the decimal point.

26. The exponent of “-3” refers to the number of times that the decimal point “moved.”.0022 is a really small number that can be rewritten using scientific notation..0022 = 2.2 x 10 -3

27. .0022 is a really small number that can be rewritten using scientific notation..0022 = 2.2 x 10 -3

28. .0022 is a really small number that can be rewritten using scientific notation. 0 022 = 2.2 x 10 -2 1 move

29. .0022 is a really small number that can be rewritten using scientific notation. 00 22 = 2.2 x 10 -1 2 moves

30. .0022 is a really small number that can be rewritten using scientific notation. 002 2 = 2.2 x 10 0 3 moves

31. .0022 is a really small number that can be rewritten using scientific notation..0022 = 2.2 x 10 -3 3 moves to the left The exponent is negative because multiplying by.001 will move the decimal to the left 3 times.

32. Rules to Write in Standard Notation If the exponent is positive, move the decimal point as many places to the right as indicated by the exponent. 1.120000 1.12 x 10 6. 1,120,000 positive exponent large number If the exponent is negative, move the decimal point as many places to the left as indicated by the exponent. 4.3 x 10 -4 0004.3.00043 negative exponent small number.

33. Example 1 Write in standard notation (decimal form). 1. Write problem. 3.0259 x 10 8 2. Write standard form. Practice A.6.7 x 10 5 B.1.38 x 10 -4 C.6.12 x 10 -5 D.5.4 x 10 4 = 670,000 =.000138 =.0000612 = 54,000

34. Rules to Write in Scientific Notation Move the decimal point to create a number greater than or equal to 1 and less than 10. Count the decimal positions to identify the exponent. If the original number is greater than or equal to 1, the exponent is positive. If the original number is between zero and 1, the exponent is negative. 3.25 x 10 6 3,250,000 use a positive exponent original number is > 1 0.0008178.17 x 10 -4 use a negative exponent original number is between 0 and 1

35. Example 2 Write in scientific notation. 1. Write problem. 42,000,000 2. Write scientific notation. Practice A.0.000052 B.3,107,000 C.970,000,000 D.0.0063 = 5.2 x 10 -5 = 3.107 x 10 6 = 9.7 x 10 8 = 6.3 x 10 -3 What do you already know about the sign of the exponent?

36. LOL Moment!

37. Operations with Scientific Notation Group the whole/decimal numbers together. Group the powers of 10 together. Simplify within each group. Write the whole/decimal number in scientific notation. Combine the powers of ten.

38. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

39. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

40. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

41. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

42. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

43. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 1. Write problem. What is left over and where is it located?

44. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem.

45. Perform the indicated operation. Write the result in scientific notation. 2. Group the whole/decimal numbers together. Group the powers of 10 together. 3. Simplify within each group. 4. Write the whole/decimal number in scientific notation. 5. Combine the powers of ten. 1. Write problem. What do you know about the size of this number?

46. Perform the indicated operation. Write the result in scientific notation. 1. Write problem. 2. Use power of product property. 3. Write the whole/decimal number in scientific notation. 4. Combine the powers of ten. What do you know about the size of this number?

47. 4) Write the missing exponent. 1) 3 x 10 ? 2) 6.8 x 10 ? 3) 3.5 x 10 ? 4) 2.45 x 10 ? = 30,000 = 680,000 =.0035 =.0000245

48. 1) 3 x 10 4 2) 6.8 x 10 ? 3) 3.5 x 10 ? 4) 2.45 x 10 ? = 30,000 = 680,000 =.0035 =.0000245 4) Write the missing exponent.

49. 1) 3 x 10 4 2) 6.8 x 10 5 3) 3.5 x 10 ? 4) 2.45 x 10 ? = 30,000 = 680,000 =.0035 =.0000245 4) Write the missing exponent.

50. 1) 3 x 10 4 2) 6.8 x 10 5 3) 3.5 x 10 -3 4) 2.45 x 10 ? = 30,000 = 680,000 =.0035 =.0000245 4) Write the missing exponent.

51. 1) 3 x 10 4 2) 6.8 x 10 5 3) 3.5 x 10 -3 4) 2.45 x 10 -5 = 30,000 = 680,000 =.0035 =.0000245 4) Write the missing exponent.

52. 5) Write each number in scientific notation. 1) 357,000 2) 6,250,000 3).00045 4).0027

53. 5) Write each number in scientific notation. 1) 357,000 2) 6,250,000 3).00045 4).0027 = 3.57 x 10 5

54. 5) Write each number in scientific notation. 1) 357,000 2) 6,250,000 3).00045 4).0027 = 3.57 x 10 5 = 6.25 x 10 6

55. 5) Write each number in scientific notation. 1) 357,000 2) 6,250,000 3).00045 4).0027 = 3.57 x 10 5 = 6.25 x 10 6 = 4.5 x 10 -4

56. 5) Write each number in scientific notation. 1) 357,000 2) 6,250,000 3).00045 4).0027 = 3.57 x 10 5 = 6.25 x 10 6 = 4.5 x 10 -4 = 2.7 x 10 -3