The excess is in that difference 23- 22.9166= 0.0834. Multiply that by the 48 you just multiplied by to get the "remainder": 0.0834(48)= 4.

Apologies since this isn't in the realm of arithmetic but rather computer science, but I don't recommend this specific approach for a very important reason...

Often times when working with calculators you'll have a repeating or infinite result (as is the case here) and the limited precision of the computer may well give you the wrong answer after multiple operations due to rounding. More elaborate calculators will consider the entire input expression, but by the time you have 22.9166666... as in this example, the damage has already been done.

In order to circumvent the potential for rounding errors, one should use an algorithm that avoids forcing the computer to round, as much as possible.

@MarkFL gave a good suggestion that isn't subject to precision rounding: multiply the integer quotient of 1100 / 48 (which is 22) by 48, then subtract the result from 1100 to find the remainder.