First, realize that you can multiply the top & bottom by 10 without changing the value of the fraction:
5.1/104 = 51/1040
Second, we're going to divide it down to the hundredth place because that's what we'll use to determine whether to round up or down.
How many times does 51 go into 1? 0
How many times does 51 go into 10? 0
How many times does 51 go into 104? 2, so if you're writing it out long-division style, you'd write the 2 above the 4 digit
And 51×2 = 102, which we subtract from 104
104 - 102 = 2, we drop down the next digit beside it to get 20.
How many times does 51 go into 20? 0, so you write 0 next to the 2 on top to get 20 (you should now have two different 20's written down just by chance)
We used up all the given digits of 1040, but we can create infinitely more in the decimal realm because 1040 = 1040.0000000.......
So tack on a ".0" next to 1040 so that you can drop down another 0 and as a result, any more digits we create in our answer will also be in the decimal realm, so tack on a "." next to the top 20 to get our tenth place.
Now we ask, how many times does 51 go into 200? 3, write that on top (you should have 20.3 so far)
And 51×3 = 153, which we subtract from 200
200 - 153 = 47, we create another 0 to have 1040.00 and drop it down to get 470
How many times does 51 go into 470? 9, write that on top & multiply just to confirm that.
51×9 = 459, so that is the largest product we would've gotten without going over.
Now we have a quotient of 20.39 and the hundredth's place tells us that we should round up to
Hope you found the wordiness helpful :)