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