Ah! I think I see what you mean. Well, I night. You mean you don't have a rough sense of what to expect of your answer without just computing it? I'm not 100% sure I do either 😛

But there's some things we can maybe do. The easiest one, in this case, is that we can temporarily play with orders of magnitude and put on a factor of 100 to get 23/7 = ~3 which means when we take that 100 back off your answer is going to be roughly -0.03. And again, that answer comes from leveraging multiplication insights, to aid division. 23 looks like 21, and I know 21 is a multiple of 7.

Any magnitude we add to our numerator is countered by any magnitude we add to our denominator. So if we had 0.23/73, we could multiply by 100 again to get 23/73, and then multiply by 10 again to get 230/73, but we can also equivalently reduce the denominator by a factor of 10, giving us 23/7 ish. We've actually moved by 3 orders of magnitude to get there, so our new "gut" answer is -0.003 ish.

That's my first guess of what you meant. But you did say you needed "actual" solutions. So maybe you didn't mean you wanted an intuition about approximations, and you actually wanted to do the long division?

Just in case, I'll do another worked example of what you might do on paper if you didn't want to use a calculator.

0.23÷7. 7 goes into 0 zero times, easy, that's our ones place solved. 7 goes into 02 zero times as well, so our answer so far is 0.0 and we're moving on to hundredths. 023 is larger than 7, and as before it is recognizably near to 21, a multiple of 7. 7×3 is 21, so our answer so far is 0.03, and our remainder is 23-21=2 (which is actually 0.02, but we keep multiplying things by 10 during the algorithm so we don't have to worry about that). Okay, we move another order of magnitude down and have 20÷7, which again looks a lot like 21, but smaller so we know it's 2. 0.032 and a remainder of 20-14=6. 60÷7 is 8, so 0.0328 and 60-56=4. 40÷7 is 5, 0.03285 with remainder 40-35=5. 50÷7 is 7, so 0.032857 and remainder 50-49=1. 10÷7 is 1, 0.0328571, with 10-7=3. 30÷7 is 4, 0.03285714, remainder 30-28=2. And now we're in trouble. Because we've already seen 2. 20÷7 is 2, remainder 6 again. So it just loops now!

-0.032857142857142857142.....

And that's less of a division problem and more of a problem with decimal numbers rather than fractions. It's simply a limitation of the way we write things. So there isn't an exact numerical answer for this particular division, you just have to decide where is enough decimal places for your application.

I don't know if any of that helped at all... but it's an attempt!