Final answer:
During numerical calculations, do not round off immediately but carry extra digits through intermediate steps, only rounding off to the required number of significant figures in the final answer. This method prevents the accumulation of rounding errors, ensuring the final result accurately represents the calculated values' certainty.
Step-by-step explanation:
In the intermediate steps of a numerical calculation, it is important to follow certain guidelines to ensure accuracy in the final result. Here are some practices that should be followed:
Do not round the result of every arithmetic operation immediately. Instead, carry as many digits as possible from the intermediate answers to the next calculation step.
Keep at least a couple of extra digits beyond those needed for determining significant figures, which can make the final answer slightly more accurate.
Only apply the rules of significant figures and round to the correct number of digits when you arrive at the final answer.
Understand the reason for these rules, which is to correctly represent the certainty of the values reported and ensure that a calculated result is not represented as being more certain than the least certain value used in the calculation.
Example of Maintaining Significant Figures
For instance, when performing the calculation (13.2 + 12.252) × (1.35 × 2.1) = 25.452 × 2.835 = 72.15642, it is rounded off to 72 in agreement with 2.835 which should have been rounded to 2.8 if it were a one-step calculation. Rounding the intermediate answers could have led to the incorrect final answer of 71 instead.