But, what if you have 12 apples and want to divide it to 12 people. Hopefully, students will arrive at the notion that dividing with decimals is actually a way of using a common denominator of 1. This solves some problems, but creates others, especially when a calculator is used. Our trouble with .3333 and such are an outgrowth of the decision to use decimals. The above raises another familiar notion, that a number can be represented in more than one form.
Some forms have a direct representation in reality.
Rounding is our way to make decimals with many digits into more friendly, shorter numbers. But, we lose some more information when we do that. I am sure other underlyting issues hide here and hope other people jump in on this discussion. Other examples work with other systems. You don't need to buy Internet access to use free Internet e-mail.