The sum of the greatest and smallest number of five digits is

### Concept & Logic The greatest $n$-digit number is formed entirely of $9$s, and the smallest $n$-digit number consists of a $1$ followed by zeros. To find their sum, we simply add the two constructed numbers. ### Step-by-Step Solution **Calculation:** 1. Determine the greatest 5-digit number: This is formed by five $9$s, which is $99999$. 2. Determine the smallest 5-digit number: This is formed by a $1$ followed by four $0$s, which is $10000$. 3. Calculate their sum: $$99999 + 10000 = 109999$$ ### Exam Strategy & Shortcut When adding $10000$ to any 5-digit number, you only need to increment the ten-thousands digit by $1$. Since $9 + 1 = 10$, write $10$ in front of the remaining $9999$ to get $109999$ instantly. ### Common Pitfall A frequent error is assuming the "smallest" 5-digit number is formed by repeating ones ($11111$), which would incorrectly lead to $99999 + 11111 = 111110$. ### Final Answer Therefore, the correct answer is **109,999**.