As the talk of ‘prefixes’ in the previous post on units suggests, physics involves working with both very large and very small numbers. While we humans are pretty good at working with numbers with rather small numbers of digits (one, two, three, even four or five digit numbers can be handled with a fair degree of precision and reliability), if we increase the number of digits to ten or twelve, then we slow way down and start making more mistakes.
To help reduce the burden of large and small numbers on we mere humans, scientists often work with numbers using what’s called scientific notation. Rather than writing a large or small number as we might normally, we split it into two parts: a mantissa and an exponent. Rather than muddy the waters with an inadequate explanation, I’ll give an example.
According to my calculator (and Google), the speed of light in a vacuum is 299,792,458 m/s. When working in scientific notation we write the speed of light as:
2.99792458 ×108 m/s.
Here ‘2.99792458’ is the mantissa and ‘8’ is the exponent. Scientific notation
means exactly what is says: take the mantissa, and multiply it by
10exponent. The multiplier is always 10, so this is the same
thing as moving the decimal point exponent places to the left or right.
Using scientific notation helps us write numbers with many non-significant digits in a more compact form (the weight of an electron, for instance, begins with thirty-one 0’s and the mass of the Earth ends with twenty 0’s), helps us determine the order of magnitude of a number (instead of counting the digits, we can just look at the exponent), and reduces the effect of transcription errors (if we skip, transpose, or mistake one of the digits in the mantissa, the number will at least be in the same order of magnitude as the original).
For more information, you might like to see the Wikipedia articles on scientific notation and order of magnitude and the Wolfram MathWorld articles on scientific notation and order of magnitude.