Simple, simple question concerning errors needing quick answer

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In summary, the question is asking for the value of z in the function f(z) that will output the value of the integral I with different levels of error. The calculated value of I is 0.6666666... recurring. For an error of 0.1, z must be 4, for an error of 0.01, z must be 7, and for an error of 0.001, z must be 9.
  • #1
T7
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Hi,

This is a v. simple Q, but I have a mental block today (!).

The question is: What size must z be in the function f(z) to output the value of the integral I with an error of 0.1? What about an error of 0.01? Or 0.001?

I calculate I to be 0.6666666... recurring.

Now

f(3) = 0.8148148147
f(4) = 0.7500000000
f(5) = 0.72000000
f(7) = 0.693875508
f(8) = 0.687500000
f(9) = 0.6831275719
f(10) = 0.6800000000

etc.

By a 0.1 error, does it mean that the value of f(x) must fall within I ± 0.1? ie no more than (0.66666... + 0.1 =) 0.76666666... and no less than (0.66666... - 0.1 =) 0.5666666 ? ie. z=4 satisfies the requirement (?)

Cheers.
 
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  • #2
Yes, that is correct. For an error of 0.01, the value of z must be 7 and for an error of 0.001, the value of z must be 9.
 

1. What are the most common types of errors in scientific experiments?

The most common types of errors in scientific experiments include human error, measurement error, sampling error, and systematic error.

2. How can I minimize errors in my experiments?

To minimize errors in your experiments, it is important to carefully plan and design your experiment, use precise and calibrated equipment, conduct multiple trials, and carefully record and analyze data.

3. What is the difference between random and systematic error?

Random error is caused by chance and can be reduced by taking multiple measurements and averaging them. Systematic error is caused by a consistent flaw in the experimental setup or equipment and can be reduced by identifying and correcting the source of the error.

4. What should I do if I discover an error in my data after completing an experiment?

If you discover an error in your data, it is important to carefully analyze the cause of the error and determine if it can be corrected. If the error cannot be corrected, it is important to report it and explain its potential impact on the results.

5. How can I determine the accuracy and precision of my measurements?

To determine the accuracy and precision of your measurements, you can compare your results to known values or conduct a series of repeated measurements. Accuracy measures how close your results are to the true or accepted value, while precision measures how close your results are to each other.

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