Estimation Techniques and Order of Magnitude Problems

One of the more useful skills that you can gain is to become adept and order of magnitude estimation (you will amaze your friends and maybe even win money from them ...:) )

This skill will also allow you to think our your feet better and to develope a more quantitative view of any problem. This helps when people are just making crap up. Being numerically literate is quite important as a crap management skill.

Today we will try a bunch of practice problems to hone our skills.

The basic rule set for doing an estimation problem is

1. Understand the problem and what is being asked

2. choose a set of consistent units

3. try to scale up a local example that your familiar with

4. devise an estimation plan

5. turn the crank on your plan

6. perform a reality check on your result; this important step is often completely forgotten In general, estimation requires multiplying things together. You can do this in your head fairly easily if you work in units of 2, or 10. Remember, this is an estimation only - estimation means a result that is good to within a factor of a few. Its an estimate. Its not an exact answer. It doesn't need to be an exact answer.
   
   A simple estimation spreadsheet
   
   I will start off by showing how to estimate the number of grains of sand on all the world's beaches. Here are the steps which you will help with:
   
   
   • Volume of a grain of sand is 1 cubic mm
   • What is the volume of a standard beach (Length, width, depth)?
   • What percentage of a coastline contains a standard beach?
   • What is the maximum length of a coastline on the Earth?
   • How many coastlines are there on the Earth?
   
   
   Once we have numbers for those, we just multiply them together.

   
   
   Now, let's work these out using the same procedures:
   
   

   1. How many gallons of gas are used in US automobiles on a daily basis?
      
      
   2. How many blood donations are there in the US per year?
      
      
   3. How many starbucks are there in the US?
      
      
   4. How many gallons of water are used annually for washing clothes in the US?
      
      
   5. How many pizzas are consumed by all the students at the University of Oregon during one academic year (9 months)?
      
      
   6. How many M&M's would be needed to cover the surface of the Matt Court basketball floor?
      
      
   7. Can the entire student body of the UO fit on the football field at Autzen Stadium?
      
      
   8. Estimate the total number of sheets of 8.5 x 11 inch paper used by all the students at the University of Oregon in an academic year.
      
      
   9. How many total miles does the United States Interstate Highway system contain?
      
      
   10. How many years would it take a common snail to traverse all of the US Coastlines?
       
       
   11. How many Douglas Fir Trees are there in Oregon?