Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information.... 
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Scientific Notation
Most of the interesting phenomena in our universe are not on the human scale. It would take about 1,000,000,000,000,000,000,000 bacteria to equal the mass of a human body. When the physicist Thomas Young discovered that light was a wave, it was back in the bad old days before scientific notation, and he was obliged to write that the time required for one vibration of the wave was 1/500 of a millionth of a millionth of a second. Scientific notation is a less awkward way to write very large and very small numbers such as these. Here's a quick review. Scientific notation means writing a number in terms of a product of something from 1 to 10 and something else that is a power of ten. For instance,
32 = 3.2 × 10^{1} Each number is ten times bigger than the previous one. Since 10^{1} is ten times smaller than 10^{2} , it makes sense to use the notation 10^{0} to stand for one, the number that is in turn ten times smaller than 10^{1} . Continuing on, we can write 10^{1} to stand for 0.1, the number ten times smaller than 10^{0} . Negative exponents are used for small numbers:
3.2 = 3.2 × 100 A common source of confusion is the notation used on the displays of many calculators. Examples:
3.2 × 10^{6} (written notation) The last example is particularly unfortunate, because 3.2^{6} really stands for the number 3.2 × 3.2 × 3.2 × 3.2 × 3.2 × 3.2 = 1074, a totally different number from 3.2 × 10^{6} = 3200000. The calculator notation should never be used in writing. It's just a way for the manufacturer to save money by making a simpler display.


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