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 10 7, then the answer is written as 7. Answers written as 3 x 10 7 will be marked as incorrect. Positive exponents are the default, for negative exponents the minus sign (-) must be included. 1.5 x is written as -3

Rounding Off five or greater (up to ) - round up 5.00 x 10 3 is written as and less … and down to one - round down 4.99 x 10 3 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 10 4 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 10 1 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 = 10 7 people Circulation = 10 6 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 ft 2 Total volume for all subscriptions = 10 6 subscriptions x.5ft 2 /subscription/week = 500,000 cu. ft/per week = 5 x 10 5 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 isnt 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