Describe two real life applications of irrational numbers

If you are to deposit a dollar at 100% interest rate per annum, then after a year the interest added to your original deposit becomes $2. If you however compound the interest each half year, so the interest added is 50% each time, then you'll end up having $2.25. Quarterly, the interest will be 25% each and you'll have about $2.44. Monthly, about $2.61.
If you keep compounding in shorter and shorter time intervals, eventually you'll tend towards an irrational sum of money after the first year, nearly $2.72, or $e.