To convert the remaining decimal numbers $169$ and $2028$ into base 13, we can proceed with the following steps:

1. Convert 169 to base 13:

   • $169 \div 13 = 13$ remainder $0$
   • $13 \div 13 = 1$ remainder $0$
   • So, $169_{10}$ in base 13 is represented as $100_{13}$.

2. Convert 2028 to base 13:

   • $2028 \div 13 = 156$ remainder $0$
   • $156 \div 13 = 12$ remainder $0$
   • $12$ in base 13 is simply represented as $C$ (since base 13 uses $0$ to $C$ where $C$ represents $12$).
   • So, $2028_{10}$ in base 13 is represented as $C00_{13}$.

Thus, the answers are:

• $169_{10} = 100_{13}$
• $2028_{10} = C00_{13}$

Would you like further explanations on these conversions, or do you have any questions?

Here are five related questions to expand on this topic:

1. How do you convert numbers from base 13 back to decimal?
2. Why is base 13 less commonly used than bases like 10, 2, and 16?
3. How do we represent letters (like $A$, $B$, and $C$) in base 13 and other bases above 10?
4. What are the practical applications of using different bases in mathematics and computing?
5. Can you explain the process of converting other base numbers, like base 7 or base 8, to decimal?

Tip: When converting numbers to a base that is not standard, always double-check if the new base requires symbols for digits beyond $9$, like using letters in base 13, 16, etc.