# Use of Scientific Notation

An explanation by means of examples.

### 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 104,
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 106253,000 = 2.53 X 100,000 = 2.53 X 1051000 = 1.0 X 1000 = 1.0 X 1031 = 1.0 X 1 = 1.0 X 100

### 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., 103 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 [1/103] 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 [1/105] = 4.0 X 10–50.016 = 1.6/100 = 1.6 X [1/100] = 1.6 X [1/102] = 1.6 X 10–2(Note how this one is simpler.) 0.01 = 1/100 = 1/102 = 1.0 X 10–20.00723 = 7.23/1000 = 7.23 X [1/1000] = 7.23 X [1/103] = 7.23 X 10–3

 Page last modified on 8/25/04 at 6:30 PM, CDT. John Lindquist, Department of Bacteriology University of Wisconsin – Madison