1. Fermi Questions
Ted Simons

2. Good general and scientific literacy
What skills?
Decent Math Skills
Good general and scientific literacy
The ability to not sweat the small stuff

3. Not Sweating the Small Stuff - What is a Fermi Question?
A question satisfied by An order-of- magnitude estimate of a value.
How many people live in the United States?

4. According to the internet a week ago:
324,700,462 people
x 108
Fermi answer is 108 or simply 8

5. Round the number appropriately:
600,000,000.
x 108
Fermi answer is 109 or simply 9

6. How many centimeters tall is Mt. Everest?
Good Literacy
How many centimeters tall is
Mt. Everest?

7. …potentially useful literacy
Mt Everest rises to 29,029’ MSL
2.54 centimeters in an inch
12 inches in a foot
Or…30.5 cm per 1 foot

8. 29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 12 𝑖𝑛𝑐ℎ𝑒𝑠 1 𝑓𝑡 × 2.54 𝑐𝑚 1 𝑓𝑡 =884,804
29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 30.5 𝑐𝑚 1 𝑓𝑡 =885,384
Sig Figs are MEANINGLESS here!
29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 12 𝑖𝑛𝑐ℎ𝑒𝑠 1 𝑓𝑡 × 2.54 𝑐𝑚 1 𝑓𝑡 =884,804
Fermi rounds both to the closest power of 10, or 106

9. What to know - MEASURES
How wide is New York State?
What is the diameter of the Earth?
How thick is a human hair?
How big is hydrogen?
How heavy is water?
What is the mass of a car?

10. What to know - CONVERSIONS
Feet to miles
Meters to miles
Centimeters to inches
Kilograms to pounds on Earth
Angstroms to meters
Liters to gallons
Moles

11. What to know - CONSTANTS
Electrons’ charge
Speed of light and sound
Gravitational constant
Planck’s constant
Boltzmann’s constant
Gas constant

12. What to know – FORMULAS/RELATIONSHIPS
Work
Electrical power
Gravitational Attraction
Ideal Gas Law
Internal energy
Bernoulli’s Equation

13. 29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 12 𝑖𝑛𝑐ℎ𝑒𝑠 1 𝑓𝑡 × 2.54 𝑐𝑚 1 𝑓𝑡 =884,804
29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 30.5 𝑐𝑚 1 𝑓𝑡 =885,384
Sig Figs are MEANINGLESS here!
29,029 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 12 𝑖𝑛𝑐ℎ𝑒𝑠 1 𝑓𝑡 × 2.54 𝑐𝑚 1 𝑓𝑡 =884,804
Fermi rounds both to the closest power of 10, or 106

14. But you have no calculator!
No Worries! Fermi is here!

15. 3× 10 4 𝑓𝑡 1 𝐸𝑣𝑒𝑟𝑒𝑠𝑡 × 3× 10 1 𝑐𝑚 1 𝑓𝑡 =9× 10 5 𝑐𝑚
= 10 6 𝑐𝑚

16. Dimensional Analysis/Unit Conversion Area, Volume, Surface Area
Decent at Math
Rounding
Exponents!
Multiply and Divide
Dimensional Analysis/Unit Conversion
Area, Volume, Surface Area
Circles, Triangles, Squares
Spheres, Cubes, Pyramids, Tetrahedrans?

17. Test Format and Scoring
Word Questions
Mixture of science and whimsical
Answer is the power of ten
Points
5 if agrees with accepted
3 if ± 1
1 if ± 2

18. Samples

19. How many ping pong balls will fit in a tractor trailer?

20. Strategy:
Divide the volume of a tractor trailer by the volume of a ping pong ball.

21. If you don’t know the size of a tractor trailer, picture it in you mind…
…maybe 3 meters tall, by 3 meters wide by 20 meters long.

22. 𝑉 𝑡𝑟𝑎𝑖𝑙𝑒𝑟 =3𝑚×3𝑚×20𝑚=200 𝑚 3
Note that I rounded 3m x 3m to 10 square meters

23. Picture a ping-pong ball
Picture a ping-pong ball. It is about 4 cm in diameter, so its radius is 2 cm (or 2 x 10-2 m!)

24. 𝑉 𝑝𝑖𝑛𝑔 = 4 3 𝜋 𝑟 3 =4× (2× 10 −2 ) 3 =4×8× 10 −6 𝑚 3 =3× 10 −5 𝑚 3
=4×8× 10 −6 𝑚 3 =3× 10 −5 𝑚 3
Note that 𝜋 3 ≈1
And 4×8≈3× 10 1

25. 𝑉 𝑡𝑟𝑎𝑖𝑙𝑒𝑟 𝑉 𝑝𝑖𝑛𝑔 = 2× 10 2 𝑚 3 3× 10 −5 𝑚 3 = 10 7

26. 𝑉 𝑡𝑟𝑎𝑖𝑙𝑒𝑟 𝑉 𝑝𝑖𝑛𝑔 = 3950 𝑓𝑡 3 1.18× 10 −3 𝑓𝑡 3
= 3.35×10 6

27. Your Turn

28. How many miles of road in the New York Interstate system?*

29. How many millimeters of thread in a high quality king-size bed sheet?

30. How many stone blocks were used to build the Great Pyramid of Giza?

31. How many electrons flow through a 100 Watt bulb at Motel 6 in a 24 hour period?

32. How many apples can you harvest from an acre of orchard?

33. How many high school seniors are in the US right now?

34. How many kittens would balance a scale with King Kong?

35. How many Hershey Kisses could you heap into the back of a standard pickup truck?

36. How many rubber molecules are lost on average per rotation of a car wheel?