50.0 centimeters means that the side was rounded to the nearest
tenth of a centimeter. Therefore the side could have been as long
as 50.04999999999 cm or as short as 49.95 centimeters. Either way,
rounded to tenths it would have been 50.0 centimeters.
It is only necessary to calculate the percentage error when the
error was due to rounding up. But let's see why that is the case.
In the first case the error would have been 50.04999999999-50.0 =
0.04999999999 and the fraction error would have been
0.04999999999/50.04999999999 and the decimal error would be
0.0009999001 and the percent error would be 0.0999999%
In the second case, the error would have been 50.0-49.95 = 0.05
centimeters, and the fraction error would have been 0.05/49.95
and the decimal error would be 0.001001... and the percent error
would be 0.1001001...%, or 0.1%
So you see, it is only necessary to calculate the percentage error
when the error was due to rounding up. That's because the percentage
error is slightly more when the error is due to rounding up than
when it is due to rounding down, and we want the maximum possible
percentage error.
Edwin
