1. The problem is to write the first $8n$ decimals of a recurring (repeating) decimal number. 2. A recurring decimal is a decimal number where a sequence of digits repeats infinitely. 3. To write the first $8n$ decimals, you need to identify the repeating block of digits. 4. Suppose the repeating block has length $k$ digits, then the decimal expansion looks like $0.\overline{a_1a_2\ldots a_k}$. 5. To write the first $8n$ decimals, repeat the block $\lceil \frac{8n}{k} \rceil$ times to ensure you have at least $8n$ digits. 6. Then truncate the decimal expansion to exactly $8n$ digits. 7. For example, if the repeating block is "123" ($k=3$) and $n=2$, then $8n=16$ decimals. 8. Repeat "123" $\lceil \frac{16}{3} \rceil = 6$ times: "123123123123123123" (18 digits). 9. Truncate to 16 digits: "1231231231231231". 10. This is the first $8n$ decimals of the recurring decimal. In summary, identify the repeating block, repeat it enough times, then truncate to $8n$ digits.