FERMI QUESTIONS

Science Olympiad Summer InstitutePhoenix, AZ

July 18 – 22, 2011

What is a Fermi Question?

A rough estimate of a quantity which is either difficult or impossible to measure directly (How many drops of water are in Lake Erie?)

Answers are given in powers of ten (exponent)

Named after Enrico Fermi

PARAMETERS

Bring pencils Calculators, computers, slide rules, reference

sheets, etc. are not allowed Teams which finish before the allotted time

should turn in their answer sheet and have the time recorded by the event supervisor

Writing AnswersCorrect power of 10 (exponent) If the estimated

answer (based on a rough calculation) is 3 x 107, then the answer is written as 7.

Answers written as 3 x 107 will be marked as incorrect.

Positive exponents are the default, for negative exponents the minus sign (-) must be included.

1.5 x 10-3 is written as -3

Rounding Off

five or greater (up to 9.99...) - round up5.00 x 103 is written as 4

4.99 and less … and down to one - round down4.99 x 103 is written as 3

SCORING

• 5 Pts – answer is equal to the accepted value• 3 pts – answer is +1 of the accepted value• pt – answer is +2 of the accepted value

What is the circumference of Earth?

One possible solution requires the answer to these two questions.

• How many time zones are there on Earth?• How many miles/time zone?

How many time zones are there on Earth?

• There are 24 hours in a day therefore there are 24 time zones

How many miles/time zone?

• The distance from New York to Los Angeles is about 3,000 miles

• Since the New York and Los Angeles are 3 time zones apart there is 1000 miles/time zone (3000 mi/3 time zones = 1000 mi/time zone)

SOLUTION

• 24 time zones x 1000 miles = 24,000 miles• 24,000 = 2.4 x 104

• Answer is written as 4

Grading Homework

What is a reasonable number of hours per week that a teacher should allocate to grade all of his students’ homework if students average 35 min./night five nights/week?

SOLUTIONAssumptions:1. 5 classes of 25 students/class2. 5 classes/day3. 5 days/week4. Grading papers takes 3 minutes eachCalculations:3 min/student x 25 students/class x 5

classes/day x 5 days/week = 1875 min/wk / 60 min/hr = 31 hr/wk = 3.1 x 101

Written as: 1

New York Times

How much paper (by volume) does the New York Times use in one week?

SOLUTION

Assumptions:• Population of New York = 107 people• Circulation = 106 papers/day (most families by

only 1 copy and not every family subscribes)• Weekday paper measures 1 ft x 1 ft x .5 in

when folded• Sunday paper measures 1 ft x 1 ft x 2 in when

folded

Solution (cont.)Calculations for one week:• 6 newspapers/day x ½”/newspaper + 2” (for the

Sunday edition) = 5”/week• Total volume/week for one subscription =

1 ft x 1 ft x 5/12ft = .5 ft2

• Total volume for all subscriptions = 106 subscriptions x .5ft2/subscription/week =500,000 cu. ft/per week = 5 x 105

Answer is written as 6

KEYS TO SUCCESS

Have good assumptions – The best assumptions are the ones you do not have to assume (size of a sheet of paper). Most often you will have to assume

Equations – There isn’t much need for accurate complex equations

Be as accurate as possible with the most questions

Partner Pairing

Estimator:• a visual/kinetic person with good memory• able to estimate the dimensions, weights, etc.

of various objects (artificial and naturally occurring

• should know random facts (frequency of a cordless phone, number of Crayola colors, demographic populations, etc.

Partner Pairing (cont.)

Number Cruncher• Performs quick calculations• Knows physical values and conversions factors

such as pounds in a kilogram, speed of light, etc.

Find and Know Many Facts

• Physics facts (speed of sound, wavelength of a color of light, etc.)

• Human body facts (size of a cell, body temp.)• Facts about your State, the United States, or the

WorldRemember, since it is impossible to know

everything, just guess. You can be off by a lot and still get the answer right (its powers of 10).

FINALLY, REMEMBER

• Being off by 50% will still give you full pts.• You can be off by as much as 250 % and still

get points.• There is no penalty for being wrong, do not

guess blindly• Sometimes it is best to round something down

if you have rounded something else up

Remember (cont.)

• Do not dwell on a single problem unless it is your last

• Keep your calculations neat and simple• Use common sense