Final answer:
The sum of 6.2174 and 0.7684 is 6.9858, rounded to four decimal places in accordance with the rules of significant figures for addition, which dictate rounding off to the least precise measurement.
Step-by-step explanation:
When calculating the sum of two numbers, 6.2174 and 0.7684, it's important to consider the precision of the numbers involved. According to the rules of significant figures for addition and subtraction, the result should not have more decimal places than the number with the least decimal places. Therefore, the sum of 6.2174 and 0.7684 would be initially calculated as 6.9858. However, due to the principles of significant figures, we need to round our result to the least precise measurement, which is four decimal places in this case. So the final rounded result is 6.9858.
Calculators will typically provide a result with more precision than necessary, for instance presenting a sum of 6.9858 without considering significant figures. It's the responsibility of the person performing the calculation to round off the final answer appropriately. In practical situations, such as measuring quantities with a specific precision, only a certain number of decimal places may be considered significant.