As a human (as far as I know...) there is a decent chance I'd write it like that, depending on the exact numbers.
It said "over 197 thousand". That's what I'd probably say for a number in [197000, 197999], or maybe "under 198 thousand depending on where it is in that range.
Saying "nearly 200 thousand" is still 3 digits so doesn't save any space over 197 or 198, and I think with it only being 3 digits most people will assume only the last digit is rounded. 200 ending in a string of 0s does suggest it might be rounded to the nearest 10 or nearest 100, but it just could easily not be.
I'd almost certainly fully write out 1816. If it were common to spell out groups below 1000 like 100s and were going to that I might write it as something like "just over 18 hundred" or "almost 19 hundred", but I almost never see anyone use grouping sizes of less than 1000.