Fermi Questions

Fermi Questions

Answer in scientific format!

Rounded to the nearest exponent.

220 = 2.2 x 10² = 2 (2 is what you would put as the answer)
1,680,000,000 = 1.68 x 10⁹ = 9


That means you should estimate the factors and make rough calculations.

How many 6th graders are there in the United States?

The U.S. population is around 300 million = 3 x 10⁸
The average lifespan is around 80 = 10²
10⁸ / 10² = 10⁶
Answer = 6

(Actual answer: 3.6 million, or 3.6 x 10⁶)

How many times does the average person’s heart beat in a lifetime?

Estimate, calculate, then round:
- Average # of heartbeats/min. = 60 = 10²
- Minutes/year = 60x24x365 = 525,600 = 10⁵
- Average lifespan = 80 years = 10²

10² x 10⁵ x 10² = 10⁹ Answer: 9

Try these! Work alone or with a partner.

Multiple Choice

How many Calories are in a gummi bear? (Calorie means kcal, the standard unit used on food packaging.)

• 10^-2

• 10^-1

• 10¹

• 10²

A gummi bear actually has 9 calories. You would need some prior knowledge to be able to accurately estimate, but if you know that 2000 kcal is the daily recommended intake, you could probably estimate that one gummi bear has to be a very small number.

9 kcal = 10¹

Multiple Choice

How many bald people are there in the world?

• 10⁸

  Answer = 8

• 10⁷

  Answer = 7

• 10⁶

  Answer = 6

• 10⁵

  Answer = 5

Population = 8 billion = 10¹⁰

Eliminate women (1/2) and men under 60 (3/4 of men), leaving 1/8 of total = 10⁹

Estimate 10% of the rest are bald = 10⁸

Multiple Choice

What is the width of your hand in miles?

• 10²

  Answer = 2

• 10⁰

  Answer = 0

• 10^-3

  Answer = -3

• 10^-5

  Answer = -5

Average hand width = 3 inches = .25 feet
Mile = 5280 feet
.25 / 5300 converts to 1 / 21200
---->Rather than do that division, you can estimate the value by counting the number of digits in the denominator. The actual answer is 0.000047

Answer = 10^-5