Giving a lecture on decimal fractions

[gummz]

I'm a little empty on what to talk about. Only things that come to mind is normality (and mentioning Pi in that respect) and that 1/number's decimal expansion is only finite if its prime factors are 2 or 5. What else is there to talk about?

 

[mfb]

Length of periods for fractions like 1/3, 1/7, ...
0.999... = 1
Different bases
History of the decimal system maybe
How to convert an arbitrary rational number from the decimal system to a fraction of integers

Depending on the scope, show that every real number can be expressed in that way and that the expression is unique apart from the 0.999... = 1 thing.