imc

We have $$\frac{1}{20^{20}}=\frac{1}{(10\cdot 2{)}^{20}}=\frac{1}{10^{20}\cdot 2^{20}}$$ Now we do some estimation. Notice that $2^{20}=1024^2$, which means that $2^{20}$ is a little more than $1000^2=1,000,000$. Multiplying it with $10^{20}$, we get that the denominator is about $1\underset{26\text{ zeros}}{\underbrace{00\dots 0}}$. Notice that when we divide $1$ by an $n$ digit number as long as n is not a power of 10, there are $n-1$ zeros before the first nonzero digit. This means that when we divide $1$ by the $27$ digit integer $1\underset{26\text{ zeros}}{\underbrace{00\dots 0}}$, there are $\boxed{\text{ 26}}$ zeros in the initial string after the decimal point.