Gaining Perspective on Valid Digits in Physics Problems

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• johann1301h
In summary, the rating "of shawshank redemtion" is 9.2, even though not one single visitor gave it 9.2 stars. This is clearly(?) an overrepresentation of data. Why is it right or acceptable to use more digits then is in the data in this case, but not when you are for example measuring the magnetic field strength around the earth, or any other emprical measurment?
johann1301h
TL;DR Summary
Discussion about number of valid digits
I am trying to gain some perspective into the topic of «number of valid digits» when doing physics problems.

I have been doing physicsproblems for å long time, but i have never really understood why the rules regarding number of digits to include in the final answer - is the way that it is.

I think the core principle behind it all is this;

DONT OVERREPRESENT DATA

And i think this again is a principle sprung out of emperical idealism/philosophy.

But then i ask, why is it so wrong to «OVERREPRESENT DATA»

Take for example the rating system at IMdB.com, for rating movies. Each visitor has a chouse between 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 stars to rate a movie. Not for instance 9.2. But yet the rating «of shawshank redemtion» is 9.2, even though not one single visitor gave it 9.2 stars. This is clearly(?) an overrepresentation of data. Why is it right or acceptable to use more digits then is in the data in this case, but not when you are for example measuring the magnetic field strength around the earth, or any other emprical measurment?

johann1301h said:
This is clearly(?) an overrepresentation of data.

Why? Movie A gets 100 9's and Movie B gets 50 9's and 50 10's. Which is the better regarded movie?

This is the way I understand it: When people select stars, that is an exact quantity, so theoretically there are an infinite number of zeros after the decimal place. Where significant figures is important is when something is measured.
So there is precision & accuracy. I'm on my phone, so I won't look them up at the moment, but I believe accuracy has to do with how well a measuring device, such as a scale behaves, and Precision has to do with what level (how many digits) you can read from the device.
If you weigh something on a scale - Suppose the scale has a level of precision of 1 gram. If it reads 50 grams, you don't really know if it is 50.49 or 49.51 do you? If you decide it is 50.000 and do some calculations, then report a bunch of digits, those extra digits are meaningless.

If you really want to get into it, find a copy of John Taylor's book, Introduction to Error Analysis.

the more digits you use to describe a quantity the more accurate your description of result of measurement is and the smaller the mean of error is. the maximum number of digits is only for readability.

johann1301h said:
Take for example the rating system at IMdB.com, for rating movies. Each visitor has a chouse between 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 stars to rate a movie. Not for instance 9.2. But yet the rating «of shawshank redemtion» is 9.2, even though not one single visitor gave it 9.2 stars. This is clearly(?) an overrepresentation of data. Why is it right or acceptable to use more digits then is in the data in this case, but not when you are for example measuring the magnetic field strength around the earth, or any other emprical measurment?

In your example, "9.2" is not necessarily an overrepresentation of data.

Suppose there are 10 raters, with 8 of them rating the movie as 10 and 2 of them rating it as a 9. Now let's compute the average rating, using the standard rules for significant figures.

Step 1: Add the individual ratings, which are all accurate to the "1s" place. The sum is 92, and we consider that accurate to the 1s place because, when we add numbers, we keep the precision -- e.g. 10s, 1s, 0.1s, etc. place -- of the least precise individual number being added.

Note that "92" has 2 significant figures, even though some ratings (the 9s) each had just 1 sig fig.

Step 2: Divide 92 by 10, the number of raters. We keep the 2 sig figs in 92, and note that the 10 is an exact number, the number of raters, and report the result as 9.2.

Ibix and russ_watters

What are valid digits in physics problems?

Valid digits in physics problems are the numbers that are considered accurate and reliable for use in calculations. These are typically numbers that have been measured or obtained through experimentation, rather than estimated or calculated.

Why is it important to gain perspective on valid digits in physics problems?

Gaining perspective on valid digits in physics problems is important because it allows us to understand the level of accuracy and precision in our calculations. This is crucial in scientific research and experimentation, as even small errors in measurements can lead to significant discrepancies in results.

How can I determine the number of valid digits in a measurement?

The number of valid digits in a measurement can be determined by looking at the instrument used to make the measurement. Each instrument has a certain level of precision, which determines the number of digits that can be reliably measured. The last digit in a measurement is always considered an estimate and should be treated as such.

What is the difference between accuracy and precision in valid digits?

Accuracy refers to how close a measurement is to the true or accepted value, while precision refers to how close multiple measurements of the same quantity are to each other. Valid digits in physics problems are both accurate and precise, meaning they are close to the true value and consistent with each other.

Can valid digits change in different calculations or experiments?

Yes, valid digits can change depending on the specific calculation or experiment being performed. This is because different instruments or methods may have different levels of precision, and therefore, different numbers of valid digits. It is important to consider the level of precision in each individual measurement when using valid digits in calculations.

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