Adding and Subtracting Significant Figures

In summary, when adding or subtracting numbers with different sig figs, the answer should be reported with the least precise number. In the given example of 43.4 - 22 - 3, the answer would be 18 since it has only one significant figure. However, to account for potential errors, the answer should be reported as 18.4 +/- 0.7.
  • #1
cvc121
61
1

Homework Statement


Hi,

To add or subtract sig figs, it is to my understanding that the answer is reported so that it reflects the least precise number.

For the example 43.4 - 22 - 3, would I report my answer as 18 or 20?
Thanks. Any help is very much appreciated!

Homework Equations

The Attempt at a Solution


The least precise number is 3 but I am not sure if I would report my answer with 1 or 2 sig figs. I am guessing that my answer should be 20 since it has only one significant figure as well.
 
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  • #2
Been a long time since I did such a thing formally but as I recall the normal practice is to say that your error is the RMS of the individual errors, which in this case would be sqrt((.05*2 + .5*2 + .5*2)/3) = .7 so your answer is 18.4 +/- .7
 

1. What are significant figures and why are they important in adding and subtracting?

Significant figures are the digits in a number that are known with certainty, plus one digit that is estimated. They are important in adding and subtracting because they help maintain the accuracy and precision of a calculation.

2. How do I determine the number of significant figures in a given number?

The general rule is to count all non-zero digits as significant figures. Zeros between non-zero digits are also significant. However, leading zeros in decimal numbers are not significant, and trailing zeros after a decimal point are significant. For example, 0.007 has two significant figures, while 0.070 has three significant figures.

3. What is the rule for adding and subtracting significant figures?

The rule is to round the result to the least number of decimal places in the original numbers. For example, if the original numbers have three decimal places, the result should also have three decimal places.

4. Can I ever have more significant figures in the result of an addition or subtraction?

No, the rule is to always round the result to the least number of significant figures in the original numbers. Having more significant figures in the result would imply a higher level of precision than what is given in the original numbers.

5. Are there any exceptions to the rule of significant figures in adding and subtracting?

Yes, there are some instances where the rule may be slightly different, depending on the situation. For example, when adding or subtracting numbers with very large or very small exponents, the rule may be to keep the same number of significant figures as the original number with the smallest number of significant figures. It is always important to follow the specific guidelines given in the problem or by your instructor.

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