Dealing with uncertainties

The exact answer is 6/100= 0.06. In summary, when doing operations with numbers with uncertainties, the resultant uncertainty should have the same number of significant figures as the resultant number. In order to do this, the largest and smallest possible values should be calculated and the resultant uncertainty should be written as the difference between these two values.
  • #1
nrslmz
15
0

Homework Statement


When doing operations with numbers with uncertainties, if the significant figures of the resultant number's uncertainty is lower the significant figures of the resultant number, how should I show the resultant uncertainty. For example,


Homework Equations


if you do the operation 5.40+-0.10 / 90.00+-0.05 , the result is
0.06+-0.001


The Attempt at a Solution


the solution must either be
0.06 +- 0.00

or

0.06 +- 0.01x(10^(-1))

since the number of the significant numbers should be equal. so which one is it?
 
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  • #2
nrslmz said:

Homework Statement


When doing operations with numbers with uncertainties, if the significant figures of the resultant number's uncertainty is lower the significant figures of the resultant number, how should I show the resultant uncertainty. For example,


Homework Equations


if you do the operation 5.40+-0.10 / 90.00+-0.05 , the result is
0.06+-0.001




The Attempt at a Solution


the solution must either be
0.06 +- 0.00

or

0.06 +- 0.01x(10^(-1))

since the number of the significant numbers should be equal. so which one is it?
That "5.40+-0.10" is a little misleading. Although 5.40 is written as if it had 3 significant figures, that +-0.10 says that is is uncertain in the tenths place and so only has 2 significant figures. One way to do this is to calculate the largest possible value: 5.5/90.05= 0.6111 and smallest value: 5.3/89.95= 0.05886 That can be written as 0.06+-0.2.
 
  • #3


As a scientist, it is important to consider uncertainties in any calculations or measurements. In this case, the number of significant figures in the resultant uncertainty should match the number of significant figures in the resultant number. This means that the solution should be 0.06 +- 0.01 instead of 0.06 +- 0.00. However, it is also important to consider the precision of your measurements and the level of uncertainty in your data. If the uncertainty is very small, it may be appropriate to use scientific notation to represent it, as in 0.06 +- 0.01x(10^(-1)). Ultimately, it is important to be consistent and clear in how you represent uncertainties in your calculations.
 

1. What are uncertainties in scientific research?

Uncertainties in scientific research refer to the potential errors or limitations in data, methods, or models that can affect the accuracy or reliability of research findings. These uncertainties can arise from various sources, such as measurement error, sampling bias, or assumptions made in the research process.

2. How do scientists deal with uncertainties in their research?

Scientists deal with uncertainties in their research by acknowledging and quantifying them through statistical analysis or sensitivity analysis. They also carefully design experiments and collect data to minimize uncertainties, and use multiple lines of evidence to support their conclusions.

3. What is the importance of addressing uncertainties in scientific research?

Addressing uncertainties in scientific research is crucial for ensuring the validity and reliability of research findings. By acknowledging and quantifying uncertainties, scientists can better understand the limitations of their results and make more informed conclusions.

4. How do uncertainties impact the interpretation of scientific findings?

Uncertainties can impact the interpretation of scientific findings by introducing doubt or variability into the results. This can lead to conflicting or inconclusive conclusions, and may require further research or analysis to address and improve the understanding of the topic.

5. Can uncertainties ever be completely eliminated in scientific research?

No, uncertainties cannot be completely eliminated in scientific research. However, scientists can work to minimize uncertainties through careful experimental design and data analysis. It is important for scientists to acknowledge and address uncertainties in their research and communicate them transparently in order to improve the understanding and reliability of scientific knowledge.

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