Suppose someone asks you the number of bits of data on a typical musical compact
Disc. In response, it is not generally expected that you would provide the
Exact number but rather an estimate, which may be expressed in scientific notation.
An order of magnitude of a number is determined as follows:
1. Express the number in scientific notation, with the multiplier of the power of
ten between 1 and 10 and a unit.
2. If the multiplier is less than 3.162 (the square root of ten), the order of magnitude
of the number is the power of ten in the scientific notation. If the
multiplier is greater than 3.162, the order of magnitude is one larger than
the power of ten in the scientific notation.
We use the symbol _ for “is on the order of.” Use the procedure above to verify
the orders of magnitude for the following lengths:
0.008 6 m ~ 102 m 0.002 1 m ~103 m 720 m ~103 m
Usually, when an order-of-magnitude estimate is made, the results are reliable to
Within about a factor of 10. If a quantity increases in value by three orders of magnitude,
Its value increases by a factor of about 103 _ 1 000.
Inaccuracies caused by guessing too low for one number are often canceled by
Other guesses that are too high. You will find that with practice your guesstimates
Become better and better. Estimation problems can be fun to work because you
Freely drop digits, venture reasonable approximations for unknown numbers,
Make simplifying assumptions, and turn the question around into something you
Can answer in your head or with minimal mathematical manipulation on paper.
Because of the simplicity of these types of calculations, they can be performed on
a small scrap of paper and are often called “back-of-the-envelope calculations.”
Taken from different books from different authors. Proper refernce will be available there !