The numbers $$2^{2024}$$ and $$5^{2024}$$ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is

The number of digits in a number $$a^b$$ is given by $$\lfloor \log_{10}(a^b)  + 1\rfloor$$

Therefore, the number of digits in $$2^{2024}$$ is $$\lfloor \log_{10} 2^{2024} +1 \rfloor = \lfloor 2024(\log_{10} 2)+1 \rfloor = \lfloor 2024*0.301 + 1 \rfloor = 610$$

And the number of digits in $$5^{2024}$$ is $$\lfloor \log_{10}{5^{2024}} +1\rfloor = \lfloor 2024(\log_{10} 5) + 1 \rfloor =\lfloor 2024*0.698 + 1\rfloor = 1415$$

Therefore, the total number of digits on the page are $$610+1415= 2025$$