Significant Digits: Estimating Next Digit

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To determine the next significant digit in a measurement of 0.1mm, one must consider the precision of the measuring instrument used. Conducting the experiment multiple times does not inherently improve accuracy if the instrument's resolution is limited. The initial assumption that 100 trials would reveal the next significant digit is flawed, as the accuracy is constrained by the instrument's capability. Ultimately, the number of trials needed to ascertain the next significant digit depends on the precision of the measuring tool rather than the quantity of measurements taken. Accurate measurement requires both a high-quality instrument and an understanding of significant digits.
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Homework Statement



Suppose you conduct an experiment in which you find a certain measurement to be 0.1mm. We have already discussed in class that this number contains 1 significant digit (the "1" to the right of the decimal), but how many times would you have to conduct the experiment in order to know the next significant digit?

Homework Equations



Significant digits

The Attempt at a Solution



My initial guess is that you would have to conduct the experiment 100 times because the next significant digit would be in the hundredths place. Is my reasoning correct?
 
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The accuracy of your measurement is only as good as the measuring instrument. For example, if you had a meter stick with no numbers but knew the stick was one meter, each measurement you made would be no more accurate than a meter no matter how many times the measurement was made.
 

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