How Should Uncertainty Impact Significant Figures in Measurements?

In summary: Your name]In summary, significant figures are used to represent the precision of a measurement, and the correct option for expressing a value with an uncertainty of +-3% of 327.76 ms-1 is (B) 327.8ms-1, rounded to 3 significant figures as 328ms-1.
  • #1
Michael_Light
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Homework Statement



The value of the speed of sound obtained in an experiment is 327.76 ms-1. The result has an uncertainty of +-3% of the result. Which one of the following values is expressed to the correct number of significant figures?

(A) 327m-1 (B)327.8ms-1 (c)328ms-1 (D)330ms-s


Homework Equations





The Attempt at a Solution



3% of 327.76 is 9.83... Isn't it? Can anyone help me with this?
 
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  • #2


Dear fellow scientist,

Thank you for bringing this question to my attention. I can see that you are struggling with understanding significant figures and how to properly express scientific measurements. Let me help you break it down.

Firstly, significant figures are a way of representing the precision of a measurement. They are the digits in a number that are known with certainty, plus one estimated digit. For example, in the number 327.76, the digits 3, 2, 7, and 7 are known with certainty, while the 6 is estimated. This means that the number has 5 significant figures.

Now, let's look at the uncertainty of +-3% of the result. This means that the actual value could be anywhere within 3% of 327.76, or between 317.93 and 337.59. To properly express this result, we need to round it to the correct number of significant figures.

(A) 327m-1 - This option only has one significant figure, which is not enough to accurately represent the precision of the measurement. We can eliminate this option.

(B) 327.8ms-1 - This option has 4 significant figures, which is more than the measured value of 327.76. We need to round it to 3 significant figures to match the precision of the measurement. Rounding to 3 significant figures gives us 328ms-1, which is the correct option.

(C) 328ms-1 - This option has 3 significant figures, which is the correct number of significant figures to represent the precision of the measurement. However, it is not the original measured value, so we cannot choose this option.

(D) 330ms-s - This option has 3 significant figures, but it is not a close enough approximation to the measured value of 327.76. We can eliminate this option.

In conclusion, the correct answer is (B) 327.8ms-1, rounded to 3 significant figures as 328ms-1. I hope this explanation helps you understand significant figures better. Keep up the good work in your scientific endeavors!
 

FAQ: How Should Uncertainty Impact Significant Figures in Measurements?

What is random uncertainty?

Random uncertainty refers to the inherent variability or imprecision in a measurement or experimental result due to factors that are beyond our control. It is caused by the unpredictable nature of the system being measured, such as random errors in instruments, environmental factors, or human error.

How is random uncertainty different from systematic uncertainty?

Systematic uncertainty, also known as systematic error, is a consistent bias or offset in measurements that can be attributed to a specific source and can be corrected or eliminated. Random uncertainty, on the other hand, cannot be corrected for and can only be minimized by repeated measurements and statistical analysis.

How do you estimate random uncertainty?

Random uncertainty is typically estimated by performing multiple measurements of the same quantity and calculating the standard deviation of the results. This provides a measure of the spread or variability of the data points, which can be used to determine the random uncertainty associated with the measurement.

Can random uncertainty be eliminated?

No, random uncertainty cannot be completely eliminated. However, it can be reduced by using more precise instruments, controlling environmental factors, and minimizing human error. Additionally, taking multiple measurements and using statistical analysis can help to mitigate the effects of random uncertainty.

How does random uncertainty affect the reliability of experimental results?

Random uncertainty can introduce a degree of imprecision or variability in experimental results, which can affect their reliability. The larger the random uncertainty, the less confident we can be in the accuracy of our measurements. It is important to consider and report the random uncertainty associated with any experimental result to provide a more accurate representation of the data.

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