Approximate numbers and rounding
I hope this is the proper spot for this! I did a little bit of searching and couldn't quite find what I was looking for, so here goes (it's more of a procedure question than a specific problem):
The chapter I'm on in my text covers calculators and approximate numbers. The rules given for operations with approximate numbers are:
1) When approximate numbers are added/subtracted the result is expressed with the precision of the least precise number (precision being the number of decimal places, if I'm reading the text correctly).
2) When approximate numbers are multiplied/divided the result is expressed with the accuracy of the least accurate number (accuracy being the total number of significant digits).
3) When the root of an approximate number is found the result is expressed with the accuracy of the number.
I'm confused about the procedure when these operations are combined, however. The text only says "where there is a combination of operations, the final operation determines how the final result is to be rounded off" with the example: (which unfortunately isn't very comprehensive). In this example I'm lead to believe that the final answer is rounded to tenths because 38.3 only has a single decimal place of precision (the final operation being subtraction), but this assumption doesn't hold true for later questions.
for example has a book answer of 253, which seems to indicate that the rounding that would take place on the multiplication before the subtraction has an effect on the final rounding. I don't think I can round at each step, though, as that would introduce error into the problem, much like chain rounding? Plus given that this is all in the context of using a calculator, it doesn't make much sense to stop at the end of each operation to round. Do I just kind of earmark the least number of significant digits if there's muliplication, then apply that to the final result? And vice-versa with the precision if the final operation is multiplication/division? I guess what I really need is a more in-depth explanation of the rounding procedures used with the mixed operations in a problem like this :)