#### Answer

$3\,492 - 3\,000 = 492 \lt 508 = 4\,000 - 3\,492$, so $3\,000$ is the rounding to the nearest thousand of $3\,492$.

#### Work Step by Step

There are two possibilities when rounding to the nearest thousand for the number $3\,492$.
Either it is $3\,000$, or $4\,000$.
To see which one is closer to $3\,492$, we look at their positive difference relatively to $3\,492$ :
$3\,492 - 3\,000 = 492$
$4\,000 - 3\,492 = 508$
Since $492 \lt 508$, $3\,000$ is closer to $3\,492$ than $4\,000$. Therefore, $3\,000$ is the rounding to the nearest thousand of $3\,492$.
For $3\,500$, we have $3\,500 - 3\,000 = 500 = 4\,000 - 3\,500$, but by convention, we round up to the bigger thousand, so $4\,000$ is the rounding to the nearest thousand of $3\,500$.