# Percentage division

Algebra Level 3

$\large {1\%} \div{2\%} \div {3\%} \div \dots \div{98\%} \div {99\%}$

If the expression above is equal to $$\dfrac{100^{a}}{b!}$$, where $$a$$ and $$b$$ are integers, find the minimum value of $$a+b$$.

×