Let's prove that this formula works.  10% as a decimal is 0.10, right?  1 times any number returns the same number.  Like 1 times $100 equals $100, right?  So, we want to see the amount gained by using 1 in front of the decimal instead of zero.  1.10 times $100 equals $110, right?  So to double money at 10% we have to have about 7 gains of 10% compounded in a row.  What if those gains happened daily, then you could double money weekly--in just 7 days.  

Day 1 $100 times 1.1 equals $110.00

Day 2 $110 times 1.1 equals $121.00

Day 3 $121 times 1.1 equals $133.10

Day 4 $133.10 times 1.1 equals $146.41