Approximating 5,617: Finding the Nearest Round Number

To solve this problem, we'll round the number $5,617$ to the nearest multiple of $1,000$ using the standard rounding rules.

Here's how we can do it:

• First, we need to look at the hundreds digit of $5,617$. This digit is $6$.
• According to the rounding rule: - If the hundreds digit is $5$ or greater, we round up. - If the hundreds digit is $4$ or less, we round down.
• Since the hundreds digit here is $6$, which is greater than $5$, we will round $5,617$ up to the nearest $1,000$.

This means $5,617$ rounds to $6,000$.

Therefore, the solution to the problem is $6,000$.