Scientific Notation

The purpose of scientific notation is to make the numbers and quantities used easier to comprehend, to read and to write.

For example, what is the mass of an electron? 

Answer: 0.000000000000000000000000000000911 kg to 3 significant figures (see sections on rounding and estimation for explanation of significant figures)

This is far too much to keep writing and anyway we'd keep losing count of all the zeros.

So we write it as a number greater than, or equal to 1, but strictly less than 10 (that is, it shouldn't equal 10), multiplied by as many tens as necessary. If you aren't comfortable using powers of numbers, now might be a good time to check the section on powers and roots. For this section it is sufficient to know that multiplying by 10 n times, is the same as multiplying by 10 to the power of n, and that dividing by 10 n times is the same as multiplying by 10 to the power of -n.

For example:

100 = 1 x 10²

4000 = 4 x 10³

568000 = 5.68 x 10⁵

and

0.5 = 5 x 10^-1

0.0686 = 6.86 x 10^-2
 
Count how many times you have to leap over digits with the decimal point to get it where you want it and that will give you the power of 10 you need.

So that mass of the electron is:

9.11 x 10^-31 to 3 significant figures.

Using scientific notation in calculations is dealt with in the section on arithmetic.

You might also want to look at the sections on powers and roots, and on bases.

Have a go at the Quiz!