SCIENTIFIC NOTATION

During this course you will encounter scientific notation. Below is a short tutorial of the most important rules.

By scientific notation we mean that we express 3,350 as 3.35 x 103, 0.00508 as 5.08 x 10-3, 1/16 as 6.75 x 10-2, etc. (There are special cases, for instance, like numbers between 1 and 100 where we usually do not bother to use scientific notation, e.g., 25 (= 2.5 x 101) and 4 (= 4 x 100).

There are specific rules about adding, subtracting, dividing and multiplying numbers expressed in scientific notation.

ADDITION and SUBTRACTION:

You must make sure that the exponents are the same before you can add or subtract numbers using scientific notation. For example, in the following example the exponents are the same to begin with (=2).

2.4 x 102  +  1.2 x 102 = (2.4 + 1.2) x 102 = 3.6 x 102
In the next example, they have to be made the same.
3.6 x 103  -  2.4 x 102 = 36 x 102  -  2.4 x 102 = (36 - 2.4) x 102 = 33.6 x 102 = 3.36 x 103.
Further examples:
1.2 x 10-2  +  2.4 x 10-1 = (0.12 + 2.4) x 10-1 = 2.52 x 10-1.
2.3  +  4.2 x 102 = (0.023 + 4.2) x 102 = 4.223 x 102.
MULTIPLICATION:

You simply multiply the mantissas and add the exponents. For example:

3.2 x 102  x  1.5 x 103 = (3.2 x 1.5) x 102+3 = 4.8 x 105.
2.6 x 10-2  x  2.2 x 103 = (2.6 x 2.2) x 10-2+3 = 5.72 x 101 (= 57.2).
DIVISION:

You simply divide the mantissas and subtract the exponents. For example:

6.6 x 103 / 2.2 x 102 = (6.6/2.2) x 103-2 = 3.0 x 101 (= 30).
4.8 x 10-2 / 1.2 x 10-3 = (4.8/1.2) x 10-2-(-3) = 4.0 x 101 (= 40).
COMPUTER NOTATION:

When working with computers and spreadsheets the x 10 is replaced by the letter E. For example:

6.6 x 103  = 6.6E3 = 6600
4.8 x 10-2  = 4.8E-2 = 0.048