Sig Figs, Still Mastering Them

  • Thread starter mircobot
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In summary, for a physics lab, the spring constant is found to be 0.1368 N/cm with an uncertainty of 5x10^-4. There may be some confusion with the scientific notation for this value. Additionally, a graph of Force vs Delta X of Spring shows two linear relationships, with one having a small slope and the other a larger slope. This is not related to the yield or ultimate strength of the nylon sheath used in the experiment. It is suggested to simply write k = 0.1368 +/- .0005 N/cm or 1.368 (+/- 0.005)x10^-1 as a clear expression of the spring constant.
  • #1
mircobot
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I know this seem pretty ridiculous to ask to such a large forum, but for my physics lab I have found a spring constant to have a value of 0.1368 N/cm with an uncertainty of 5x10^-4. How do I express the spring constant?

So far I think it is (13.68 +/- 0.05)x10^-2 N/cm but the scientific notation is wrong on the 0.1368 value.

Also, on a side note. For my lab I made a graph Force vs Delta X of Spring. We used a nylon sheath and put mass on the end of it and recorded the distance stretched. The graph shows two linear relationships. One linear slope that starts up with a very small slop, and then suddenly jerks to the right to another linear relationship with a larger slope. My professor has already told me that it has nothing to do with the yield or ultimate strength of the nylon sheath. Any ideas to help me out?

Thanks for your time.
 
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  • #2
I don't think there is anything wrong with simply writing k = 0.1368 +/- .0005 N/cm. That's how I would personally write it, but I know how labs can be pretty strict on these sorts of procedures.
 
  • #3
probably 1.368 (+/- 0.005)x10^-1 but i would prefer evict's as clearer
 

What are significant figures?

Significant figures, also known as sig figs, are the digits in a number that are considered to be accurate and reliable. They are used to express the precision of a measurement or calculation.

Why are significant figures important?

Significant figures are important because they help us determine the level of precision in a measurement or calculation. They also ensure that the results of an experiment or calculation are reported accurately and consistently.

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

The first step in determining the number of significant figures in a number is to identify the non-zero digits. These are always considered to be significant. The next step is to count the number of zeros between the first non-zero digit and the last non-zero digit. These zeros are also significant. Finally, any zeros at the end of a decimal number after the last non-zero digit are significant. Zeros at the beginning of a decimal number are not significant.

What is the rule for rounding numbers with significant figures?

When rounding numbers with significant figures, the general rule is to round to the same number of significant figures as the number with the least number of significant figures in the calculation. If the digit to be dropped is less than 5, the preceding digit remains unchanged. If the digit to be dropped is 5 or greater, the preceding digit is increased by one.

How do you perform calculations with significant figures?

When performing calculations with significant figures, the result should be rounded to the same number of significant figures as the number with the least number of significant figures in the calculation. Intermediate results should be carried out to one or two extra digits to avoid rounding errors. In addition, when multiplying or dividing, the final answer should have the same number of significant figures as the number with the least number of significant figures. When adding or subtracting, the final answer should be rounded to the same number of decimal places as the number with the least number of decimal places.

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