Unit 2: Working with Radicals

Name: ______Date: ______Color: ______

Unit 2: Working with Radicals

Scientific Notation

1. Is 0.5 x 106 written in scientific notation? Explain why or why not. 0.5 x 106 is not written in scientific notation because for a number to be written in scientific notation the number being multiplied by 10 can have one and only one non-zero number before the decimal point.
2. Is 7.89 x 106 between 0 and 1 or greater than 1? Explain how you know. 7.89 x 106 is greater than 1 because 7.89 x 106 is the same as 7890,000 which is greater than 1.

Write the number in scientific notation.

3. 8.5 4. 0.72 5. 82.4

No movement à1 place ß 1 place

8.5 x 100 7.2 x 10-1 8.24 x 101

6. 0.005 7. 72,000,000 8. 0.00406

à3 places ß 7 places à 3 places

5 x 10-3 7.2 x 107 4.06 x 10-3

9. 1,065,250 10. 0.000045 11. 1,060,000,000

ß 6 places à 5 places ß 9 places

1.06525 x 106 4.5 x 10-5 1.06 x 109

12. 0.00000526 13. 900,000,000,000,000 14. 0.00000007008

à6 places ß 14 places à8 places

5.26 x 10-6 9 x 1014 7.008 x 10-8

15. Which number represents 54,004,000,000 written in scientific notation?

54,004,000,000

ß 10 places

A. 54004 x 106 B. 54.004 x 109 C. 5.4004 x 1010 D. 0.54004 x 1011

Write the number in standard form.

16. 2.6 x 103 17. 7.5 x 107 18. 1.11 x 102

à3 places à 7 places à 2 places

2,600 75,000,000 111

19. 3.03 x 104 20. 4.709 x 106 21. 1.544 x 1010

à 4 places à 6 places à 10 places

30,300 4,709,000 15,444,000,000

22. 6.1 x 10-3 23. 4.4 x 10-10 24. 2.23 x 10-6

ß 3 places ß 10 places ß 6 places

0.0061 0.00000000044 0.00000223

25. 8.52 x 10-8 26. 6.4111 x 10-10 27. 1.2034 x 10-6

ß 8 places ß 10 places ß 6 places

0.0000000852 0.00000000064111 0.0000012034

28. Describe and correct the error in writing 1.24 x 10-3 in standard form. When the number was re-written in standard form the decimal was moved to the right when it should have been moved to the left (.00124)

Order the numbers from least to greatest.

29. 45,000; 6.7 x 103; 12,439; 2 x 104

6,700 20,000

6.7 x 103; 12,439; 2 x 104; 45,000

30. 65,000,000; 6.2 x 106; 3.557 x 107; 55,004,000; 6.07 x 106

6,200,000 35,570,000 6,070,000

6.07 x 106; 6.2 x 106; 3.557 x 107; 55,004,000; 65,000,000

31. 0.0005; 9.8 x 10-6; 5 x 10-3; 0.00008; 0.04065; 8.2 x 10-3

0.0000095 0.005 0.0082

9.8 x 10-6; 0.00008; 0.0005; 5 x 10-3; 8.2 x 10-3; 0.04065

Complete the statement using <, >, or =.

32. 5.6 x 103 56,000 33. 404,000.1 4.04001 x 105

5,600 404,001

34. 9.86 x 10-3 = 0.00986 35. 0.003309 = 3.309 x 10-3

0.00986 0.003309

36. 2.203 x 10-4 > 0.0000203 37. 604,589,000 > 6.04589 x 107

0.000203 60,458,900

Evaluate the expression. Write your answer in scientific notation.

38. (4.4 x 103)(1.5 x 10-7) 39. (7.3 x 10-5)(5.8 x 102) 40. (8.1 x 10-4)(9 x 10-6)

4.4(1.5) = 6.6 7.3(5.8) = 42.34 8.1(9) = 72.9

3 + (-7) = -4 -5 + 2 = -3 -4 + (-6) = -10

6.6 x 10-4 42.34 x 10-3 72.9 x 10-10

ß 1 place ß 1 place 4.234 x 10-2 7.29 x 10-9

41. 6 x 10-3 42. 5.4 x 10-5 43. 4.1 x 104

8 x 10-6 1.8 x 10-2 8.2 x 108

6 ÷ 8 = .75 5.4 ÷ 1.8 = 3 4.1 ÷ 8.2 = .5

-3 – (-6) = 3 -5 – (-2) = -3 4 – 8 = -4

.75 x 103 3 x 10-3 .5 x 10-4

à 1 place à 1 place

7.5 x 102 5 x 10-5

44. (5 x 10-8)3 45. (7 x 10-5)4 46. (1.4 x 103)2

53 = 125 74 = 2,401 (1.4)2 = 1.96

-8(3) = -24 -5(4) = -20 3(2) = 6

125 x 10-24 2401 x 10-20 1.96 x 106

ß 2 places ß3 places

1.25 x 10-22 2.401 x 10-17

47. Which number is the value of 1.235 x 104

9.5 x 107

1.235 ÷ 9.5 = .13

4 – 7 = -3

.13 x 10-3

à 1 place

1.3 x 10-4

A. 0.13 x 10-4 B. 1.3 x 10-4 C. 1.3 x 10-3 D. 0.13 x 103

48. The spacecrafts Voyager 1 and Voyager 2 were launched in 1977 to gather data about our solar system. As of March 12, 2004, Voyager 1 had traveled a total distance of about 9,643,000,000 miles, and Voyager 2 had traveled a total of about 9.065 x 109 miles. Which spacecraft had traveled the greater distance at the time? Voyager 1

Voyager 1 = 9,643,000,000

Voyager 2 = 9.065 x 109 = à 9 places = 9,065,000,000

49. In 2002, about 9.7 x 108 pounds of cotton were produced in California. The cotton was planted on 6.9 x 105 acres of land. What was the average number of pounds of cotton produced per acre? Round your answer to the nearest whole number.

9.7 x 108 9.7 ÷ 6.9 = 1.0405797101

6.9 x 105 8 – 8 = 3

1.405797101 x 103

1405.797101

1,406 pounds per acre

50. The average flow rate of the Amazon River is about 7.6 x 106 cubic feet per second. The average flow rate of the Mississippi River is about 5.53 x 105 cubic feet per second. Find the ratio of the flow rate of the Amazon to the flow rate of the Mississippi. Round your answer to the nearest whole number. What does the ratio tell you?

7.6 x 106 7.6 ÷ 5.53 = 1.374321881

5.53 x 105 6 – 5 = 1

1.374321881 x 101

13.74321881 ≈ 14

The flow of the Amazon River is approximately 14 times faster than the Mississippi River