The Question: Why must a calculated answear generally be rounded?
My Answear: A calulated answear cannot be more precise than the least precise measurement from which it was calculated.
I think your answer is ok but I think you are leaving out information that should be included. I would add a sentence something like this---put it in your own words. "Calculators and manual calculations may provide many more digits than are significant; thus, rounding is necessary to prevent a false impression." I would leave your first sentence as is.
You are right, my initial answer does provide a general reason for rounding, but it doesn't explain the specific reasons for rounding in calculations. I appreciate your suggestion to include more information.
To provide a more complete explanation, when we perform calculations using numbers that have been measured or rounded themselves, there is inherent uncertainty or imprecision in those numbers. This uncertainty can arise from various sources, such as measurement instruments with limited precision or the inherent limitations of decimal representation.
Calculators and manual calculations often provide calculations with more decimal places than are actually significant. For example, if we measure the length of an object using a ruler with markings up to millimeters, our measurement might be something like 12.573 millimeters. However, the ruler's precision only goes up to the nearest millimeter, so the actual precision of the measurement would be ±0.5 mm.
When we perform calculations using the measured value, the uncertainty or imprecision in the initial measurement propagates through the calculations. Therefore, the calculated answer cannot be more precise than the least precise measurement from which it was obtained.
Rounding the calculated answer is necessary to prevent a false impression of precision. By rounding to an appropriate number of significant figures, we can communicate the level of uncertainty or imprecision associated with our calculation. Rounding allows us to convey the calculated answer in a concise and meaningful way, without misleading others about the level of precision or accuracy.