2024/004) Find the smallest a and b such that $\frac{1}{640} = \frac{a}{10^b}$

We have $640= 128 * 5 =  2^7 * 5$

To make it a power of 10 we need to multiply by $5^6$ giving $10^7$

so $a=5^6$ and b = 7 are the smallest values