Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

Why including more digits in answers, does not make it more accurate?

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• oubaas
Lv 7
2 months ago

It could to a certain extent , otherwise which would be the reason of giving PI or g with a large number of decimals ?

If i want to calculate very precisely the circonference of a circle whose given radius is 5.0001 , then i wont approximate PI to 3.14 : i will use 3.1416 or 3.14159.

If, instead,  the given radius is 5.01 , then PI = 3.14 is enough

• 2 months ago

Let's say I'm weighing something and my scale has a precision of 0.1 grams. I might weigh something and find that its weight reads 47.3 grams. Therefore, the weight read by my scale is somewhere between 47.25 and 47.35 grams (otherwise, my scale would have read a different number). So if I say that the weight is 47.31415926535, how is that any more accurate than 47.3 grams?

Now imagine that I have an expensive, highly accurate scale with precision to 0.0001 grams' Using that scale, I find the weight of the same object to be 47.4826 grams. We can see that, to one decimal of precision, the correct weight is 47.5 grams. Now think about those additional digits that were applied to the weight of the lesser quality scale. Do you see how absolutely meaningless the additional precision is? It doesn't matter if I say that the weight is 47.3 grams or 47.31415926535 grams. Both answers are _inaccurate_ despite the additional precision, since the true weight is much closer to 47.5 grams.

• 2 months ago

Every measurement made by equipment in the real world has an accuracy. Those numbers need to be carried through any calculations in order to determine the final accuracy. No matter how many extra digits you can get out of your calculator or other computer program, those digits are just noise, and don't mean anything.

Often times, it's not important to know the final exact accuracy, a good rule of thumb is to limit answers to three significant digits.

• 2 months ago

Physics is an experimental subject.  If the figures have been obtained by experiment there is a certain accuracy.  ie a certain level of trustworthiness in the answer.  Correctly this is expressed as a bound.  eg  5.2 < x < 5.4

The value can be anwhere in between these.  So we say x = 5.3 (+- 0.1)

Now if you WRITE that x = 5.312543786 do you know anything more than you did?  The only thing you know is that it is STILL somewhere between 5.2 and 5.4 and no matter how many digits you write you cannot alter that accuracy of the experiment itself.

• Jim
Lv 7
2 months ago

More digits than are significant are just lies!!!

• 2 months ago

In measuring things we have two considerations: the accuracy of the measurement and the precision of the measurement.  And in concept, they are the antithesis of each other.  Which is to say as we increase precision, we make it more likely that our measurement is inaccurate.

When you increase the number of digits, the number of decimal points, you are making your measurement more precise, more fine.   So, for example, 71.33 deg F has a precision in the hundredths of degrees Fahrenheit.  And 71 deg F is precise to single degrees so it's less precise than the 71.33 deg F.

Now you walk outside to take the dog for a walk.  The air is brisk and you think, "It feels like it's in the 70's today."  And you'd be correct, it is accurate to think that because 71.33 and 71 degrees are both in the 70's range.  But if you thought, "It feels like it's 71.34 deg F today," you'd be inaccurate because it's actually 71.33 deg.

And there you are.  You added two decimal points to make the guess of temperature more precise, but in doing that made your guess wrong, inaccurate.

Bottom line, if your measuring stick is imprecise, trying to use it to measure with more precision will only lead to making more errors in accuracy.

• 2 months ago

because the extra digits may be meaningless. If you read 10 volts on a 1% meter, that means the value is between 9.9 and 10.1 volts. Expressing it as 10.000 volts is meaningless10.0 is the best you can do.

• Scott
Lv 6
2 months ago

Because if you do not know the correct answer to a question, increasing the length of your response will not make it more accurate.

• Rick
Lv 7
2 months ago

I have no idea what that has to do with anything either ............