Simple Uncertainty/Sig Fig Question

  • Thread starter Badgeray
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In summary, for a lab assignment involving subtracting two values and adding uncertainty, the decimal places of the uncertainty should match those of the value. In this specific example, the answer would be 35.7mL ± 0.15mL, although it may seem odd to have one pair of values with two decimal places and the other with only one. Additionally, it is generally recommended to take a statistical approach and use the root sum square of the errors, and the number of decimal places in the answer should not exceed the worst case input value.
  • #1
Badgeray
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Homework Statement


This is for a lab. I have two values that I need to subtract, so I am pretty sure I am supposed to add up uncertainty. I have also been told that the uncertainty decimal places should match up with the decimal places on the value itself.

50.00mL ± 0.05mL – 14.3mL ± 0.1mL =

Homework Equations

The Attempt at a Solution


35.7mL ± 0.15mL?
 
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  • #2
Matching up the decimal places between error and value is generally right, why do you know one pair of values to two decimal places and the other pair to only one? It seems odd.
Assuming there is a good reason for that, there are two more points to consider. Generally,one argues that you would be unlucky for the errors to reinforce to the maximum extent, so instead take a statistical approach. Specifically, take the root sum square of the errors. Next, you cannot quote more decimal places in the answer than your worst case input value.
 

What is simple uncertainty/sig fig?

Simple uncertainty/sig fig refers to the measurement of a quantity and the estimated level of uncertainty or error associated with that measurement. Sig fig stands for significant figures, which are the digits in a number that are known with certainty plus one estimated digit.

Why is it important to consider uncertainty/sig figs in scientific measurements?

Uncertainty/sig figs are important because they reflect the accuracy and precision of a measurement. They help scientists communicate the level of confidence in their data and ensure that results are not misrepresented. Additionally, calculations involving measurements with different levels of uncertainty/sig figs must be done with consideration to the lowest level of uncertainty/sig figs in order to maintain accuracy.

How do you determine the number of sig figs in a measurement?

The general rule for determining sig figs is to start counting from the left and stop at the first non-zero digit. Then, count all the digits after that to the right, including zeros. There are also specific rules for determining sig figs in certain situations, such as when dealing with decimal points or when using scientific notation.

What is the difference between accuracy and precision?

Accuracy refers to how close a measurement is to the true or accepted value, while precision refers to how close multiple measurements are to each other. A measurement can be precise but not accurate, meaning that the results are consistent but not necessarily correct. On the other hand, a measurement can be accurate but not precise, meaning that it is close to the accepted value but not consistent with other measurements.

Can sig figs be added or subtracted?

When adding or subtracting values, the result should have the same number of decimal places as the value with the fewest decimal places. This is because adding or subtracting values with different levels of precision can result in a less precise answer. For example, if you add 5.2 and 6.345, the answer should be rounded to 5.2 since it has the fewest number of decimal places. However, if you are multiplying or dividing values, you should use the lowest number of sig figs in the calculation to determine the number of sig figs in the answer.

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