Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Is the number written in scientific notation? If not, explain.

11. 44 × 10 8 44 times , 10 to the eighth
12. 3.2 × 10 6 3.2 times , 10 to the sixth
13. 0.9 × 10 − 2 0.9 times , 10 super negative 2 end super
14. 6.7 × 1000 9 6.7 times , 1000 to the ninth
15. 7.3 × 10 − 5 7.3 times , 10 super negative 5 end super
16. 1.12 × 10 1 1.12 , times , 10 to the first
17. 457 × 10 7 457 times , 10 to the seventh
18. 9.54 × 10 15 9.54 , times , 10 to the fifteenth

See Problem 2.

Write each number in scientific notation.

19. 9,040,000,000
20. 0.02
21. 9.3 million
22. 21,700
23. 0.00325
24. 8,003,000
25. 0.00092
26. 0.0156

See Problem 3.

Write each number in standard notation.

27. 5 × 10 2 5 times , 10 squared
28. 7.45 × 10 2 7.45 , times , 10 squared
29. 2.04 × 10 3 2.04 , times , 10 cubed
30. 7.2 × 10 6 7.2 times , 10 to the sixth
31. 8.97 × 10 − 1 8.97 , times , 10 super negative 1 end super
32. 1.3 × 10 0 1.3 times , 10 to the
33. 2.74 × 10 5 2.74 , times , 10 to the fifth
34. 4.8 × 10 − 3 4.8 times , 10 super negative 3 end super

See Problems 4 and 5.

Order the numbers in each list from least to greatest.

35. 9 × 10 − 7 , 8 × 10 − 8 , 7 × 10 − 6 , 6 × 10 − 10 9 times , 10 super negative 7 end super , comma 8 times , 10 super negative 8 end super , comma 7 times , 10 super negative 6 end super , comma 6 times . 10 super negative 10 end super
36. 8.2 × 10 5 , 7.9 × 10 5 , 2.7 × 10 5 , 8.1 × 10 5 8.2 times , 10 to the fifth , comma 7.9 times , 10 to the fifth , comma 2.7 times , 10 to the fifth , comma 8.1 times , 10 to the fifth
37. 50.1 × 10 − 3 , 4.8 × 10 − 3 , 0.52 × 10 − 3 , 56 × 10 − 3 50.1 , times , 10 super negative 3 end super , comma 4.8 times , 10 super negative 3 end super , comma , 0.52 , times , 10 super negative 3 end super , comma 56 times , 10 super negative 3 end super
38. 0.53 × 10 7 , 5300 × 10 − 1 , 5.3 × 10 5 , 530 × 10 8 0.53 , times , 10 to the seventh , comma , 5300 , times , 10 super negative 1 end super , comma 5.3 times , 10 to the fifth , comma 530 times , 10 to the eighth
39. Physics The half-life of a radioactive isotope is the amount of time it takes one half of a sample of the isotope to decay. What is the order of the following radioactive isotopes of uranium from shortest to longest half-life?

B Apply

Simplify. Write each answer using scientific notation.

40. 4 ( 2 × 10 − 3 ) 4 open 2 times , 10 super negative 3 end super , close
41. 8 ( 3 × 10 14 ) 8 open 3 times , 10 to the fourteenth , close
42. 0.2 ( 3 × 10 2 ) 0.2 open 3 times , 10 squared , close
43. 6 ( 5.3 × 10 − 4 ) 6 open 5.3 times , 10 super negative 4 end super , close
44. 0.3 ( 8.2 × 10 − 3 ) 0.3 open 8.2 times , 10 super negative 3 end super , close
45. 0.5 ( 6.8 × 10 5 ) 0.5 open 6.8 times , 10 to the fifth , close

46. Think About a Plan A light-year is the distance light travels in one year. One light-year is about 5,878,000,000,000 mi. The table shows the estimated distance, in light-years, of several stars from Earth. How many miles is each star from Earth?

    • How do you convert from light-years to miles?
    • What notation is easier to use for writing long distances?
47. Writing You write 1 billion in scientific notation as 10 9 . 10 to the ninth , .  Explain why you write 436 billion in scientific notation as 4.36 × 10 11 4.36 , times , 10 to the eleventh  rather than as 436 × 10 9 . 436 times , 10 to the ninth , .

SOURCE: NASA

Table of Contents