'Fractioning' Fractions

Lets 'complexify' the fractions by writing it down using simple operations:

$\frac{1}{2}$ = 1/2 , $\frac{2}{3}$ = 2/3 , $\frac{3}{4}$ = 3/4 , ... $\frac{98}{99}$ = 98/99 , $\frac{99}{100}$ = 99/100

/ means division and * means multiplication

Our result of 'complexifying' the fractions should be 1/2 2/3 3/4..98/99*99/100

Observe that from the first two fractions it is 1÷2*2÷3 and we notice the 2's get cancelled because they are the same number with an inverse operation. So we get $\frac{1}{blank}$ times $\frac{blank}{3}$ and following the same procedure we cancel the 3's , the 4's and so on until we get 1 as the only numerator left and 100 as the only denominator left so we can put the one above the 100 like this $\frac{1}{100}$ which is equivalent to 0.01 and that is the answer.