Order of Magnitude and EstimationSyllabus statements 1.1.1-1.1.4—due Wednesday, 9/19/12
Warm-up/Journal question:
How many plain M&M’s would it take to fill a beaker like the one on the front counter? On your warm-up sheet:▪ Estimate your answer, and explain HOW
you reached your estimation. Write estimated answers for each person
in your group on your whiteboard (numbers ONLY…no names with them!)
Estimated calculation--example
NO CALCULATORS! Estimate the answer to the following:
Work with your group—come up with one answer that you write on your group whiteboard.
14
5
(3728) (470165 10 )
(278146) (0.000713 10 )
“Fermi Questions”
What is the approximate circumference of the Earth? Use what you know in order to estimate
an answer! NO calculators!
Image from: http://www.spacetoday.org/Satellites/TerraAqua/TerraStory.html
Fermi Question Assignment: As a group, do this on your whiteboard… Draw a Fermi Question out of the bowl. Estimate an answer to your question SHOW how you got your answer
Order of Magnitude (OM) Always written as a whole number
power of ten (i.e. There are ~106
people living in the Seattle area) The OM is the power of ten that is
“closest” to the value you are estimating
OM values are not very precise! They are an ESTIMATE!
But they DO give us a general idea about the magnitude (size) of a value
Video: Powers of 10
Order of Magnitude (OM) If an approximate (or known) value
can be determined, an Order of Magnitude can be calculated
OM values are only used to determine rough estimates
But HOW?? Let’s use the following example…
Population of Washington State
According to the Census Bureau, the population of Washington in 2011 was 6,830,080 people.
The population growth rate between 2010 and 2011 was +1.6%/year
Based on this information, what, approximately, is the state’s population today?
For our example:
Step 1:
Step 2: round z to nearest whole
number
Step 3:
So… z = log(6,939,361) = 6.841 7
OM = 107 people in the state of WA
zOM = 10
)(VALUELogz
Using OM in ratios—comparisons
Quite often, OM values are used when comparing the sizes of 2 different measurements.
For example, How much larger than the US
population is the World’s population?
Use the information from THIS WEBSITE to answer this question
Population Ratio:
US Population: OM = ? World population: OM = ?
The population of the world is approximately 102 times larger than the population of the US
28
10
1010
10
onUSpopulati
ationWORLDpopul