## Microbial Mathematics

Because prokaryotes are very tiny and can multiply to very large numbers of cells in short time periods, convenient and simple ways are used to designate their numbers without resorting to many zeros before or after the number. In the study of microbiology, it is important to gain an understanding of the metric system, which is used in scientific measurements.

The basic unit of measure is the meter, which is equal to about 39 inches. All other units are fractions of a meter:

1 decimeter is one tenth =0.1 meter 1 centimeter is one hundredth = 0.01 meter 1 millimeter is one thousandth = 0.001 meter

Because prokaryotes are much smaller than a millimeter, even smaller units of measure are used. A millionth of a meter is a micrometer = 0.000001 meter, and is abbreviated mm. This is the most frequently used size measurement in microbiology, since bacteria are in this size range. For comparison, a human hair is about 75 mm wide.

Since it is inconvenient to write so many zeros in front of the 1, an easier way of denoting the same number is through the use of superscript, or exponential, numbers (exponents). One hundred dollars can be written 102 dollars. The 10 is called the base number and the 2 is the exponent. Conversely, one hundredth of a dollar is 10:2 dollars; thus the exponent is negative. The base most commonly used in biology is 10 (which is designated as log10). The above information can be summarized as follows:

1 millimeter = 1 mm = 0.001 meter = 10:3 meter 1 micrometer = 1 mm = 0.000001 meter = 10:6 meter 1 nanometer = 1 nm = 0.000000001 meter = 10:9 meter

The same prefix designations can be used for weights. The basic unit of weight is the gram, abbreviated g. Approximately 450 grams are in a pound.

1 milligram = 1 mg = 0.001 gram = 10:3 g 1 microgram =1 mg = 0.000001 gram = 10:6 g

1 nanogram =1 ng = 0.000000001 gram = 10:9 g 1 picogram = 1 pg = 0.000000000001 gram = 10:12 g

Note that the number of zeros before the 1 is one less than the exponent.

The value of the number is obtained by multiplying the base by itself the number of times indicated by the exponent.

Thus, 101 = 10 x 1 = 10 102 = 10 x 10 = 100 103 = 10 x 10 x 10 = 1,000

When the exponent is negative, the base and exponent are divided into 1.

When multiplying numbers having exponents to the same base, the exponents are added.

When dividing numbers having exponents to the same base, the exponents are subtracted.

In both cases, only if the bases are the same can the exponents be added or subtracted. 