What is the 1000th digit to the right of the decimal point when $\frac{4}{15}$ is expressed as a decimal?
Using long division, we find that $\frac{4}{15}=0.2\overline{6}$. Therefore, every digit to the right of the decimal point besides the $2$ in the tenths place will be $6$. The 1000th digit to the right of the decimal point is $\boxed{6}$.