FERMI QUESTIONS
Science Olympiad Summer Institute
Phoenix, 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 Answers
Correct 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 up
5.00 x 103 is written as 4
4.99 and less … and down to one - round down
4.99 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?
SOLUTION
Assumptions:
1. 5 classes of 25 students/class
2. 5 classes/day
3. 5 days/week
4. Grading papers takes 3 minutes each
Calculations:
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
World
Remember, 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