Significant Figures with Experimental Values

In summary, there is a conversation about choosing a value with the appropriate number of significant figures. The suggestion is to choose 0.74 according to sig figs, but it is also important to consider the precision of the equipment and the consistency of the other numbers. There is also a recommendation to re-do the experiment due to a large spread in the measured values.
  • #1
i_love_science
80
2
Homework Statement
I have a group of experimental numbers: 0.320, 0.910, 0.030, 0.070, and 0.080. I have to add another number to this group, which is also an experimental value. Which one should I use: 0.738, 0.740, or 0.74?
Relevant Equations
sigfigs
I was thinking of choosing 0.740, because it looks the most consistent with the other numbers because they all have a trailing zero. But then, in accordance with sig figs, 0.74 is the right answer. Which one should I choose?
Thank you so much!
 
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  • #2
It depends upon the measurement . If the previous numbers are appropriately reported on the same apparatus, then 3 sig fig is still appropriate. But I don't know which value.
 
  • #3
i_love_science said:
in accordance with sig figs, 0.74 is the right answer
No, it is the right answer only if you declare that your equipment only produces that degree of accuracy. If you know that it produces 3 significant digits then a trailing 0 is a significant digit.
 
  • #4
Did you obtain all of these readings, or did someone else record the existing ones? It is very suspicious that they all have a trailing zero - unless there is some inherent discreteness in the exact values.

Each value should be recorded with the precision it merits. If you are confident your new reading is between 0.7375 and 0.7385 then record it as 0.738.
 
  • #5
i_love_science said:
I have a group of experimental numbers: 0.320, 0.910, 0.030, 0.070, and 0.080. I have to add another number to this group, which is also an experimental value. Which one should I use: 0.738, 0.740, or 0.74?
I know this is a semi-old thread, but hopefully the answer was that you should re-do the experiment. That's a terrible spread of measured values. Look for loose screws or something in your measuring apparatus... :wink:
 
  • #6
berkeman said:
I know this is a semi-old thread, but hopefully the answer was that you should re-do the experiment. That's a terrible spread of measured values. Look for loose screws or something in your measuring apparatus... :wink:
They are not necessarily readings of the same underlying value. Maybe points on a graph.
 
  • Informative
Likes berkeman

What are significant figures and why are they important in experimental values?

Significant figures are the digits in a number that carry meaning and contribute to the precision of a measurement. They are important in experimental values because they indicate the level of accuracy and reliability of the data collected.

How do you determine the number of significant figures in a measurement?

The general rule is to count all non-zero digits as significant figures, as well as any zeros between non-zero digits. Trailing zeros after a decimal point are also significant. Leading zeros before a non-zero digit are not significant and are used only to indicate the decimal place.

What is the significance of rounding when dealing with significant figures?

Rounding is important in maintaining the appropriate number of significant figures in a measurement. When rounding, the final digit should be rounded up if it is 5 or greater, and rounded down if it is 4 or less. This helps to ensure that the measurement is not over or underrepresented.

How do significant figures affect mathematical operations in experimental values?

In mathematical operations, the result should have the same number of significant figures as the measurement with the least number of significant figures. This helps to maintain the accuracy and precision of the data and prevent overestimation or underestimation.

What are some common errors that can occur when dealing with significant figures in experimental values?

Some common errors include not counting leading zeros as significant figures, rounding incorrectly, and not carrying the correct number of significant figures through mathematical operations. It is important to be mindful of these potential errors to ensure accurate and reliable data in experiments.

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