The Physics
Hypertextbook
Opus in profectus

# Order of Magnitude

## Problems

### practice

1. Write something.
2. Write something.
3. Drake Equation
4. Write something completely different.

### investigative

1. Identify an everyday object or event that has, to the nearest order of magnitude, …
1. a length of about 1 m (or height or width or thickness)
2. a mass of about 1 kg
3. a duration of about 1 s
No "wise guy" answers like a meterstick, a one kilogram bag of flour, or the time between ticks on a clock.

### numerical

1. For your enjoyment, here's a compendium of order of magnitude questions from the New York State Regents Exam in Physics.
1. What is the approximate thickness of this piece of paper?
1. 101 m
2. 100 m
3. 10−2 m
4. 10−4 m
2. Which is the most likely mass of a high school student?
1. 1 kg
2. 5 kg
3. 60 kg
4. 250 kg
3. mass of a chicken egg
4. height of a doorknob
5. dimensions of a classroom door
6. The approximate mass of a nickel is…
1. 0.0005 kg
2. 0.005 kg
3. 0.5 kg
4. 5 kg
7. There was no order of magnitude question on this exam.
8. The weight of an apple is closest to…
1. 10−2 N
2. 100 N
3. 102 N
4. 104 N
9. The length of a high school physics classroom is probably closest to…
1. 10−2 m
2. 10−1 m
3. 101 m
4. 104 m
10. What is the approximate diameter of a dinner plate?
1. 0.0025 m
2. 0.025 m
3. 0.25 m
4. 2.5 m
11. The mass of a physics textbook is closest to…
1. 103 kg
2. 101 kg
3. 100 kg
4. 10−2 kg
12. Which object weighs approximately 1 newton?
1. dime
2. paper clip
3. physics student
4. golf ball?
13. The maximum time allowed for the completion of this [3 hour Regents] examination is approximately…
1. 102 s
2. 103 s
3. 104 s
4. 105 s
14. A mass of one kilogram of nickels has a monetary value in United States dollars of approximately…
1. \$1.00
2. \$0.10
3. \$10.00
4. \$1000.00
15. The thickness of one page of this test booklet is closest to…
1. 10−4 m
2. 10−2 m
3. 100 m
4. 102 m
16. Which measurement of an average classroom door is closest to 1 meter?
1. thickness
2. width
3. height
4. surface area
17. What is the approximate mass of a pencil?
1. 5.0 × 10−3 kg
2. 5.0 × 10−1 kg
3. 5.0 × 100 kg
4. 5.0 × 101 kg
18. There was no order of magnitude question on this exam.
19. The mass of a high school football player is approximately…
1. 100 kg
2. 101 kg
3. 102 kg
4. 103 kg
20. What is the approximate width of a person's little finger?
1. 1 m
2. 0.1 m
3. 0.01 m
4. 0.001 m
21. A high school physics student is sitting in a seat reading this question. The magnitude of the force with which the seat is pushing up on the student to support him is closest to…
1. 0 N
2. 60 N
3. 600 N
4. 6,000 N
22. The diameter of a United States penny is closest to…
1. 100 m
2. 10−1 m
3. 10−2 m
4. 10−3 m
23. An egg is dropped from a third-story window. The distance the egg falls from the window to the ground is closest to…
1. 100 m
2. 101 m
3. 102 m
4. 103 m
24. The approximate height of a 12-ounce can of root beer is…
1. 1.3 × 10−3 m
2. 1.3 × 10−1 m
3. 1.3 × 100 m
4. 1.3 × 101 m
25. What is the approximate mass of an automobile?
1. 101 kg
2. 102 kg
3. 103 kg
4. 106 kg
26. The length of a dollar bill is approximately…
1. 1.5 × 10−2 m
2. 1.5 × 10−1 m
3. 1.5 × 101 m
4. 1.5 × 102 m
27. Which wavelength is in the infrared range of the electromagnetic spectrum?
1. 100 nm
2. 100 mm
3. 100 m
4. 100 μm
28. What is the approximate length of a baseball bat?
1. 10−1 m
2. 100 m
3. 101 m
4. 102 m
29. The weight of a chicken egg is most nearly equal to…
1. 10−3 N
2. 10−2 N
3. 100 N
4. 102 N
30. The mass of a paper clip is approximately…
1. 1 × 106 kg
2. 1 × 103 kg
3. 1 × 10−3 kg
4. 1 × 10−6 kg
31. There was no order of magnitude question on this exam.
32. The work done in lifting an apple one meter near Earth's surface is approximately…
1. 1 J
2. 0.01 J
3. 100 J
4. 1,000 J
33. There was no order of magnitude question on this exam.
34. There was no order of magnitude question on this exam.
35. There was no order of magnitude question on this exam.
36. Auroras over the polar regions of Earth are caused by collisions between charged particles from the Sun and atoms in Earth's atmosphere. The charged particles give energy to the atoms, exciting them from their lowest available energy level, the ground state, to higher energy levels, excited states. Most atoms return to their ground state within 10. nanoseconds.

In the higher regions of Earth's atmosphere, where there are fewer interatom collisions, a few of the atoms remain in excited states for longer times. For example, oxygen atoms remain in an excited state for up to 1.0 second. These atoms account for the greenish and red glows of the auroras. As these oxygen atoms return to their ground state, they emit green photons (ƒ = 5.38 × 1014 Hz) and red photons (ƒ = 4.76 × 1014 Hz). These emissions last long enough to produce the changing aurora phenomenon.

What is the order of magnitude of the time, in seconds, that most atoms spend in an excited state?
37. The height of a 30 story building is approximately…
1. 100 m
2. 101 m
3. 102 m
4. 103 m
38. The diameter of an automobile tire is closest to…
1. 10−2 m
2. 100 m
3. 101 m
4. 102 m
39. Which measurement is closest to 1 × 10−2 m?
1. diameter of an atom
2. width of a student's finger
3. length of a football field
4. height of a schoolteacher
2. Perform an error of magnitude calculation to determine the approximate value of the following quantities in SI units without using a calculator.
1. surface area of a door
2. lifetime of an average human
3. Perform the following calculations using a scientific calculator. State your answer in scientific notation with a reasonable number of significant digits.
1. (6.00 × 107) × (7.00 × 106) = 4.20 × 1014

2.  2.56 × 103 = 3.20 × 10−7 8.0 × 109
3.  2.56 × 103 = 8.53 × 10−10 3.0 × 1012
4. 1,234 × 5,678 = 7.01 × 106

5. (1.60 × 10−19)2 = 2.56 × 10−38

6. √(8.98 × 1016) = 3.00 × 108

7.  (2.06 × 106) + (4.1 × 106) = 9.89 × 10−1 (3.0 × 106) + (3.23 × 106)
8.  (4.13 × 103)(2.12 × 108) = 3.27 × 10−1 (1.13 × 107)(2.37 × 105)
9.  8.60 × 107 = 2.60 × 105 3.31 × 102
10.  5.3 × 10−3 = 2.48 × 108 2.14 × 10−11
11. (6.07 × 107) × (7.64 × 106) = 4.64 × 1014

12. (3.28 × 107) × (5.93 × 106) = 1.95 × 1014

13. (1.99 × 10−4)2 + (6.424 × 10−4)2 = 4.52 × 10−7

14. √(9,402,000,000 × 617,700,000) = 2.41 × 109

15.  (609 × 103)2 = 6.39 × 10−3 (58 × 1012)
16.  (0.67 × 103)(1.73 × 103) = 1.72 × 10−10 (82.2 × 106)2