Plant Physiology (Biology 327)  - Dr. Stephen G. Saupe;  College of St. Benedict/ St. John's University;  Biology Department; Collegeville, MN  56321; (320) 363 - 2782; (320) 363 - 3202, fax;    ssaupe@csbsju.edu

Scientific Notation

Large or small numbers may be more conveniently expressed using scientific notation. A number expressed in scientific notation is comprised of: (1) a digit term which is usually not less than one or greater than ten; and (2) an exponent term that consists of 10 with an exponent. The exponent is determined by the number of places the decimal is shifted to the left or right to produce the digit term. A positive exponent results when the decimal is shifted to the left (the number is greater than one); a negative exponent is shifted to the right (the number is smaller than one.

The following are some examples of scientific notation:

 1,000,000 = 1 x 106 5,765 = 5.765 x 103 10 = 1 x 101 0.035 = 3.5 x 10-2 1 = 1 x 100 15 = 1.5 x 101 0.1 = 1 x 10-1 0.00000176 = 1.76 x 10-6 0.01 = 1 x 10-2

Adding Numbers expressed in scientific notation:

Convert all the numbers to the same power of 10; add the digit terms of the numbers.
Ex:   (5 x 10-6) + ( 2 x 10-4) = (5 x 10-6) + (200 x 10-6) = 205 x 10-6

Subtracting Numbers expressed in scientific notation:

Convert the numbers to the same power of 10; subtract the digit terms.
Ex:  (7 x 105) - (4 x 103) = (7 x 105) - (0.04 x 105) = 6.96 x 105

Multiplying Numbers expressed in scientific notation:

Multiply digit numbers. Add exponents.
Ex: (5.0 x 10-4) x (3.0 x 102) = (5 x 3) x 10(-4 + 2) = 15 x 10-2 = 0.15

Dividing Numbers expressed in scientific notation:

Divide digit numbers. Subtract exponents.
Ex:  (4.0 x 106) /
(2.0 x 10-2) = (4/2) x 10(6-(-2)) = 2 x 108

This was adapted from Haney, A., E. Dole, and C. Dunn. 1978. Plants and Life. A Lab Manual. McMillian, NY.

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Last updated:  01/07/2009     � Copyright  by SG Saupe