Scientific notation is used to shorten standard numbers with extremely large and small values to make them easier to read and write.
Typically scientific notation, as its name suggests, only comes up in the context of a science, such as physics, astrophysics, engineering, or chemistry. Outside of doing some kind of science where you have to deal with billions and billions of something, or a very tiny fraction of something, most day-to-day math doesn't need to use scientific notation.
In our daily number system, we use zeroes as place-holders to denote a place value system. This is actually an innovation; ancient counting systems did not express zero, instead using different stand-alone digits to represent orders of magnitude. You may be familiar with Roman numerals, where 'X,' 'C,' and 'M' to represent 10, 100, and 1000 respectively. This was efficient for expressing nice round integers, but grew complicated when attempting exact math. Our place value system allows us to get by with ten digits to express an infinite range of numbers.
However, once we've pushed the boundaries of science and calculation out a bit farther, it becomes equally cumbersome to express a number such as one quintillion as 1,000,000,000,000,000,000. This is unlikely to be a number that comes up when you're counting sheep in a flock or figuring your household budget but becomes a common number in computing the storage space of a supercomputer, estimating the distance to another galaxy, or projecting the population growth of all the plankton in the world.
It's very simple: We take the original number, and truncate as many zeroes as we can, expressing them at the end as an exponent of ten.
10 = 1e+1
100 = 1e+2
1000 = 1e+3
10,000,000 = 1e+7
56,000,000 = 5.6e+7
1,234,567 = 1.234567e+6
0.1 = 1e-1
0.01 = 1e-2
0.0051 = 5.1e-3
Note that if the original number contains no zeroes, the result will actually be longer. Notice also that more than one non-zero digit gets preserved as a decimal. We always take the original number and place a decimal point to the right of the most significant digit. For numbers smaller than 1, we express it as a negative exponent of ten instead. For an example like 8.9e+4, we expand it to ( 8.9 * ( 10 ^ 4 )) = 89,000.
A familiar non-scientific notation frequently used in business is to abbreviate 1000 (one thousand) as 'K' and 1,000,000 (one million) as 'M.' It's common to see a number like 6,100,000 expressed as "6.1M," a variation on the scientific notation.
Scientific notation is a handy method of throwing large numbers around without making them take up too much space. Use them sparingly, however, unless you're in a scientific context.
