The chapter started off with giving an introduction to a scientist and engineer by the name of Enrico Fermi. He was involved with the Manhattan Project, the project involved with creating and testing the first nuclear weapons. When the nuclear weapon was test Fermi estimated that the explosion was 10 kilotons in strength, and it is noted that it was a very close estimation indeed. The chapter goes on to say that Fermi went to go teach at the University of Chicago and he would give his students problems with very little information regarding those problems and they were named Fermi Problems. An example of a Fermi Problem would be estimating the total numbers of hairs on your head, and the number of drops of water in the great lakes (examples given in book).
In section 5.1 it talks about General Hints for Estimation. It talks about orders of magnitude which is used when you compare two very different things, such as a small rock and a planet (example given in book). The most common usage of this is the factors of 10. You could say that 1000 has three orders of magnitude, 10^3. It is said that a "ballpark" value is good enough then it comes to an input parameter. It fully depends on the topic to tell if it is safer to err on the high side or the low side. You can always improve your estimate if you cancel the errors out. And to sum 5.1 up it discusses how estimation skills become much better with experience.
Estimation by Analogy is a strategy for estimating that involves using comparison to something that you have measured previously or knowing the dimension. It is said that this strategy is best learned by learning and memorizing a number of comparison measures for each quantity you want to estimate. A good example of this is trying to estimate the size of a laptop. Because laptops were called "notebook" computers it is safe to take the measurement of a piece of notebook paper (8.5in x 11in) to compare (example given in book).
Estimation by Aggregation is another strategy for estimating that requires adding up the estimate of its parts. You can use multiplication for similarly sized parts. An example would be to estimate how much money the students at my school spend on pizza each year (example given in book).
Estimation by Upper and Lower Bounds is an important part of estimating that involves knowing if your estimate is high or low. It usually involves making a conservative estimate, which considers the worst case scenario. The worst case scenario can be either in the upper or the lower bounds depending on the certain situation. If you were estimating how much paint you would need to paint your walls you would want to be a little more in the upper bounds so that you have enough paint but not too much to where you are spending more money than you need to spend.
Estimation using Modeling is used when the estimation is more complicated or when you need a more precise estimation. You may have to use mathematical models and statistics when it comes to this kind of estimation. Also dimensionless quantities are useful sometimes. The relationship of small number variables is needed sometimes. Even in some cases extrapolating even a single variable from data is all that is needed. An example would be to calculate what would be the longest sunflower seed in a group of one billion seeds (example used from book).
Significant
Figures are the digits considered reliable in result of
measurement and calculation. I am also learning this in chemistry for the most
part I am not quite sure how alike these two topics are. The number of decimal
digits are the digits located to the right of the decimal place. Non-zero
digits are always significant, if a zero is located between two non-zero
numbers it is significant, a zero is not significant when it is used to fix a
decimal place and when it can be expressed using scientific notation. If you
are multiplying or dividing it is appropriate to use the number with the fewest
significant digits. An addition example would be 1725.463 + 489.2 + 16.73 =
1931.393, the correctly rounded answer would be 1931.4. Let the digits be the
same throughout the entire problem, if it the value is unnecessary keep it
above two significant digits. 9/5 = .56.
Reasonableness can be defined as two
different kinds of reasonableness. Physically reasonable is when the answer
makes sense in the light of our understanding of the physical situation being
explored or the estimates made. Reasonable precision is when the number of
digits make sense with the level of accuracy and precision. Accuracy is the measure of how close a
calculation or measurement came to the actual value. Repeatability is the measure of how close together different measurement
of the same parameter. Precision is
the combination of accuracy and repeatability.
Scientific
Notification is usually expressed using the format
#.### x 10^N, where the digit to the left of the decimal point is the significant
non-zero. Multiplying 10^N shows true place of decimal point. Whereas, Engineering Notation is expressed with
###.### x 10^M, where M is the integer at a multiple of three. The number of
digits left to the decimal point is either 1, 2, or 3 as needed to yield a
power of 10 that is a multiple of three.
Calculator
E-notation is basically saying that it is better to
use the format of 1.00 x 10^-3 not 1.00E -3 because you may get confused by the
lowercase e in the calculator which does not express notation.
Engineers need a quick precision so it is necessary to
use the constant with three or more digits. Thus they do not use harder to read
fractions.
