Fermi Questions
Sunday, December 30, 2007
Check out the new header!
The days of a plain, boring title are over! Blogger makes it very easy to add your own image in the header, so I decided to take advantage of this feature. I easily made the dusty chalkboard image in Photoshop using textured brushes. I feel that this new header fits well with the theme of my blog, and I hope you enjoy it! Have a happy New Year!
Friday, December 28, 2007
FQ#4-Television
If every
FA#3-Leaves, Part II
Sorry about the hiatus; here's the answer to the most recent FQ. Multiply the amount of leaves (~10,000 ) by their mass per leaf (0.45359237 kg/leaf)(source). The answer is 4 ,535 .9 kg, which is the total mass of the leaves. Multiply the total mass of the leaves by their energy output per kilogram (1,000 ,000 Joules /kg). Our answer comes to 4 ,535 ,900 ,000 Joules . Just one more step; convert Joules to (chemist's) calories
Saturday, December 8, 2007
How to: Easy Multiplication on Paper
While answering a Fermi Question, you will probably have to complete a complex multiplication problem. I don't blame you if you forgot how to do long multiplication on paper; calculators are so easily accessible (cell phones, for example) and convenient to use. But now, you have been stripped of your ability to use a calculator! You must learn how to do multiplication on paper again! Don't fear, I will now teach you about an easier way to do long multiplication: Lattice Multiplication.
Let's say we want to do this problem: 4367*1289. Now on a piece of scratch paper draw a grid with diagonals like so. (The number of rows and columns correspond to the number of digits in the numbers being multiplied, in this case 4X4.)
Now write your numbers on the outside of the grid, as shown.
Next, cross-multiply the numbers on the outside of the grid, as shown. If the result is a single-digit number than you record it with a zero in front.
Finally, add up the numbers in the diagonals, starting at the top, right corner working down and left. Record the answer on the outside of the box by the end of the diagonal. If the answer has multiple digits, record the number ones place and carry over the remaining digits to the next diagonal.
The answer comes out to be 5,629,063. A quick check on a calculator reveals this to be correct. I like to use this system because it is simple and easy to remember. The system can be adapted to do just about any multiplication problem. Next time you find yourself facing a tough multiplication problem, you will be glad that you know how to do long multiplication!
Let's say we want to do this problem: 4367*1289. Now on a piece of scratch paper draw a grid with diagonals like so. (The number of rows and columns correspond to the number of digits in the numbers being multiplied, in this case 4X4.)
Now write your numbers on the outside of the grid, as shown.
Next, cross-multiply the numbers on the outside of the grid, as shown. If the result is a single-digit number than you record it with a zero in front.
Finally, add up the numbers in the diagonals, starting at the top, right corner working down and left. Record the answer on the outside of the box by the end of the diagonal. If the answer has multiple digits, record the number ones place and carry over the remaining digits to the next diagonal.
The answer comes out to be 5,629,063. A quick check on a calculator reveals this to be correct. I like to use this system because it is simple and easy to remember. The system can be adapted to do just about any multiplication problem. Next time you find yourself facing a tough multiplication problem, you will be glad that you know how to do long multiplication!
Friday, December 7, 2007
FQ#3-Leaves, Part II
FA#2-Leaves
Estimate the average area of an American lawn (~200 sq.m) and multiply that by an estimated number of leaves per square meter (~50 leaves/sq.m). 200*50=10,000 or 1E4, so FA#2 is 4.
Friday, November 30, 2007
FA #1-Black Friday
Take the population of America (~300,000,000) and multiply that by the fraction of Americans who will go shopping (24/100). The answer is: 300,000,000*(24/100)=72,000,000 or 7.2E7. So FA#1 = 7.
Friday, November 23, 2007
Sunday, October 28, 2007
Getting Started
What are Fermi Questions and how do you solve them?
A Fermi Question is an order of magnitude estimation. For example; I want to estimate the number of leaves on my lawn. I estimate that there are about 300 leaves on the lawn. The answer is the order of magnitude. For example: 300=3*10^2. The answer is 2. When you solve a fermi question, please use a pencil and scrap paper. After you have made an estimate, then you may use a calculator and internet research to answer the question. Every Friday, a new question and the answer to last week's will be posted. I will explain how I got my answer, but if you want to dispute it, please speak up!
If you need more help, please visit this site:
http://www.soinc.org/events/fermiq/fermiguide.htm
A Fermi Question is an order of magnitude estimation. For example; I want to estimate the number of leaves on my lawn. I estimate that there are about 300 leaves on the lawn. The answer is the order of magnitude. For example: 300=3*10^2. The answer is 2. When you solve a fermi question, please use a pencil and scrap paper. After you have made an estimate, then you may use a calculator and internet research to answer the question. Every Friday, a new question and the answer to last week's will be posted. I will explain how I got my answer, but if you want to dispute it, please speak up!
If you need more help, please visit this site:
http://www.soinc.org/events/fermiq/fermiguide.htm
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