jlindquist.comBact. 102: Use of Scientific Notation
Bacteriology 102: Use of Scientific Notation An Explanation by Means of ExamplesFrom a really old handout which appeared to help at the time. | |
The aim is to express any number (for example: 46,700) in this form:
So 46,700 = 467 X 100 = 4.67 X 10,000 = 4.67 X 10^{4},
backwards and forwards.
Following the above example, these numbers are converted to scientific notation as follows:
4,000,000 = 4.0 X 1,000,000 = 4.0 X 10^{6} 253,000 = 2.53 X 100,000 = 2.53 X 10^{5} 1000 = 1.0 X 1000 = 1.0 X 10^{3} 1 = 1.0 X 1 = 1.0 X 10^{0} |
For numbers less than 1 (for example: 0.0035), a negative exponent will be used:
To change 0.0035 to a number with one digit before the decimal point, one moves the decimal point to the right three places, thus making 3.5 which is 1000 times (i.e., 10^{3} times) greater than 0.0035. To compensate, we can divide 3.5 by 1000 which amounts to multiplying 3.5 by 1/1000, subsequently getting 3.5 X [1/10^{3}] and 3.5 X 10^{–3}.
Likewise, these decimals are converted to scientific notation:
0.000043 = 4.3/100,000 = 4.3 X [1/100,000] = 4.3 X [1/10^{5}] = 4.0 X 10^{–5} 0.016 = 1.6/100 = 1.6 X [1/100] = 1.6 X [1/10^{2}] = 1.6 X 10^{–2} (Note how this one is simpler.) 0.01 = 1/100 = 1/10^{2} = 1.0 X 10^{–2} 0.00723 = 7.23/1000 = 7.23 X [1/1000] = 7.23 X [1/10^{3}] = 7.23 X 10^{–3} |