# Sig Figs when the Uncertainty is Larger than the Values

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In summary, when calculating significant figures with an uncertainty larger than the value, the uncertain digit should be used as the last significant figure. When rounding, the uncertain digit should be used to determine whether to round up or down. When adding or subtracting with large uncertainties, the final answer should have the same number of decimal places as the value with the fewest decimal places. When multiplying or dividing with large uncertainties, the final answer should have the same number of significant figures as the value with the fewest significant figures. Even when the uncertainty is larger than the value, it is important to use significant figures to accurately represent the measurement's precision.
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Homework Statement
Sig Figs when Uncertainty is Larger than Values
Relevant Equations
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Hey, so in my lab I took some apparently bad data and when I averaged it and took the standard deviation I got values for the SD that were larger than the average of the data. I'm sure they still want sig figs in the results but I'm not sure how to report it.

My average is -0.7101 and my standard deviation is 1.7506..

What is wrong with -0.7 +/- 1.8 or -1 +/- 2?

Bystander

## 1. What are significant figures (sig figs)?

Significant figures are the digits in a number that represent the precision or accuracy of a measurement. They are used to indicate the level of uncertainty in a measurement.

## 2. How are significant figures calculated when the uncertainty is larger than the values?

When the uncertainty is larger than the values, the significant figures are determined by the number of digits in the value with the least amount of uncertainty. For example, if a value has an uncertainty of 0.01 and another value has an uncertainty of 0.001, the first value would have 2 significant figures and the second value would have 3 significant figures.

## 3. Can significant figures be used for exact numbers?

No, significant figures are only used for measured or calculated numbers. Exact numbers, such as counting numbers or defined constants, have an infinite number of significant figures and do not need to be rounded.

## 4. How do significant figures affect mathematical operations?

In mathematical operations, the answer should have the same number of significant figures as the value with the least amount of significant figures. When adding or subtracting, the answer should be rounded to the least number of decimal places. When multiplying or dividing, the answer should be rounded to the least number of significant figures.

## 5. Why are significant figures important in science?

Significant figures are important in science because they indicate the precision and accuracy of a measurement. They help scientists communicate the level of uncertainty in their data and ensure that calculations are performed correctly. This helps to maintain the integrity and reliability of scientific research.

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