Noticing that $2^{10}=1024 \approx 1000$ allows for a good estimate. Alternatively, the number of decimal digits of $n$ is given by $\left\lfloor\log _{10}(n)\right\rfloor+1$. Using $\log _{10}(2) \approx 0.31$ also gives the correct answer. The exact value of $2^{41}$ is 2199023255552.