∞ generated and posted on 2015.12.29 ∞
Means of representing the extent to which a number or expression is multiplied by itself as employed, e.g., such as when diluting or in the form of scientific notation.
| An Exponent denotes the extent to which you either multiply a number by itself (in the case of whole-number exponents), take the root of a number (in the case of fractional exponents), or multiply by itself (or take the root of) the reciprocal of a number (in the case of negative exponents). |
Exponents represent an extremely powerful means of handling numbers, essentially the means by which large or small numbers are handled in science, and represent an absolutely crucial aspect of microbiology since, if for no other reason, large numbers of organisms are routinely described or handled in microbiology. See also exponential growth, serial dilution, and logarithmic decline phase.
Thus, rather than saying one-million bacteria, instead one says 106 bacteria. Or, instead of saying that one has reduced the concentration of organisms by 10,000-fold, one instead says that one has reduced the concentration of organisms by 104-fold.
In the latter example, if one started with 109 bacteria/ml and wanted to reduce that number to 105 bacteria/ml, then one would multiply 109 by 10-4 which is the same thing as dividing 109 by 104. Note that 109 × 10−4 = 109 × (1/104) = 109 ÷ 104 = 109 − 4 = 105.
Working with exponents – gasp! – described in song:
Scientific notation – gasp! – also described in a song:
And here is some more on scientific notation, without the auto-tuning:
The following video provides a short overview of exponents and diluting from a microbiological perspective:
The following video provides a short overview of exponents and serial dilution, also from a microbiological perspective: