By Ariel Balter, Ph.D. Updated Aug 30, 2022
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When combining measurements with different levels of precision, accuracy cannot be artificially increased. Instead, calculations must follow rules rooted in the concept of significant figures.
For addition and subtraction, the result should be rounded to the least precise decimal place among the operands. This ensures the final figure reflects the true precision of the data.
Consider two scales: one measures to 0.1 g and the other to 0.001 g. If you weigh 2.3 g on the first scale and 0.011 g on the second, the combined mass depends on the scale you read it on. On the 0.1 g scale it remains 2.3 g, whereas on the 0.001 g scale it could be 2.311, 2.298, or 2.342 g. Since the only information available is the two original masses, the result must be expressed with the least number of decimal places—here, one. Thus 2.3 + 0.011 = 2.3 g.
Other examples: 100.19 + 1 = 101, 100.49 + 1 = 101, 100.51 + 1 = 102. In the case of 0.034 + 0.0154, the sum is 0.050, preserving three decimal places because the trailing zero is significant. If the first number is written as 0.0340, the sum becomes 0.0494, keeping four decimal places because the zero after the four is significant.
By always rounding to the least precise decimal place, you ensure that your calculations truly represent the precision of the input data.
