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- Thread starter FizixFreak
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In summary, there is a difference between working with physical measurements in calculations and using integers in pure mathematics. In physics, the general advice is to give the answer to the least number of significant figures in the data supplied. The value of 4 in the given example should be expressed as 4.0m to be consistent. In an experiment, the uncertainty of a measurement can affect the certainty of the calculated result. Therefore, it is important to express values to a suitable degree of certainty in order to reduce uncertainty in the final answer.

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16 meters squared would be correct if the dimensions were measured to be 4.0 meters. So in this case the correct answer is 2 x 10^1 meters squared (if you mean the area of one of the square sides on the box). If you mean the volume of the box then we calculate 4 x 4 x 4 = 64 meters cubed. So then the correct answer would be 6 x 10^1 meters cubed or 6 x 10^7 centimeters cubed (as you already learned it has to be rounded to the same amount of significant figures as the measurement with the smallest amount of significant figures). Don't forget you must use the unrounded result if any further calculations have to be done with it. The final answer has to be rounded the same way again.

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There are 2 different considerations here.FizixFreak said:

Normally in problem calculations in physics, we are given numbers to put into equations and calculate answers. The general advice given is as you say. Give the answer to the least number of significant figures in the data supplied. The data supplied, on the other hand, should be consistent. The value in your example should (would?) be stated as 4.0m

On the other hand, we also use values measured in experiments to calculate something else using a formula, possibly. Here the treatment is different.

It's contradictory if the value of 4m you "obtained" for the length was only certain to ±1m

As it is written it's a bit ambiguous. Having said that, if you want to carry through your calculation, you could say that the value of 4±1 has a 25% uncertainty. [± 1 in 4]

When you square it you increase the uncertainty to 50%

Your final value of 16 could be quoted as having a 50% uncertainty, that is, ±8

16±8m²

You can look at it another way:

If the initial value is 4±1m then it could possibly be 3m or 5m

3x3 is 9 and 5x5 is 25

So your result could be anywhere between 9m² and 25m². This is almost the same result as using the percentages.

The lesson is, if you want your answer of 16, you need to express the value of 4 to a suitable degree of certainty.

PS On the other hand, if you're a mathematician and dealing only with integers, there is no problem. 4²=16 every time!

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Stonebridge said:There are 2 different considerations here.

Normally in problem calculations in physics, we are given numbers to put into equations and calculate answers. The general advice given is as you say. Give the answer to the least number of significant figures in the data supplied. The data supplied, on the other hand, should be consistent. The value in your example should (would?) be stated as 4.0m

On the other hand, we also use values measured in experiments to calculate something else using a formula, possibly. Here the treatment is different.

It's contradictory if the value of 4m you "obtained" for the length was only certain to ±1m

As it is written it's a bit ambiguous. Having said that, if you want to carry through your calculation, you could say that the value of 4±1 has a 25% uncertainty. [± 1 in 4]

When you square it you increase the uncertainty to 50%

Your final value of 16 could be quoted as having a 50% uncertainty, that is, ±8

16±8m²

You can look at it another way:

If the initial value is 4±1m then it could possibly be 3m or 5m

3x3 is 9 and 5x5 is 25

So your result could be anywhere between 9m² and 25m². This is almost the same result as using the percentages.

The lesson is, if you want your answer of 16, you need to express the value of 4 to a suitable degree of certainty.

PS On the other hand, if you're a mathematician and dealing only with integers, there is no problem. 4²=16 every time!

why would you consider that the values measured in an controlled enviorment have so much uncertainty ?

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FizixFreak said:why would you consider that the values measured in an controlled enviorment have so much uncertainty ?

I wouldn't. It's just an example.

In an experiment, if the value of 4 was obtained by measurement, there would have be a corresponding value of the uncertainty quoted. 4±something. That something would, in turn, determine how confident you are of the value of 4 squared.

To confidently give the result 16±something, you would need to have measured the value of the length of the side to be at least 4.0 ±something

As I said, there is a difference between working with physical measurements in calculations, and using integers in pure mathematics. As an integer, 4 is 4±nothing. It's known to absolute precision.

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Stonebridge said:I wouldn't. It's just an example.

In an experiment, if the value of 4 was obtained by measurement, there would have be a corresponding value of the uncertainty quoted. 4±something. That something would, in turn, determine how confident you are of the value of 4 squared.

To confidently give the result 16±something, you would need to have measured the value of the length of the side to be at least 4.0 ±something

As I said, there is a difference between working with physical measurements in calculations, and using integers in pure mathematics. As an integer, 4 is 4±nothing. It's known to absolute precision.

so what you are saying is that the measurements always have some amount of uncertainty related to them if we add or subtract that uncertainty for example for the length of a wire measured 4m we will 4+or- the uncertainty which will give another digit meaning that we can afford to have more than one digit in the result of an experiment in which we may use this measurement right ?

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If you use such a measurement to calculate something else, then that final calculation has a corresponding uncertainty associated with it.

The more accurate your original measurement, the more accurate your final calculation.

As a general rule, the more (legitimate) significant figures you have in the original value, the more you can have in the final calculation.

The point I was making is that you shouldn't get this mixed up with purely mathematical calculations such as what is 4 X 4? The answer is exactly 16 because the original value of 4 is not subject to any uncertainty. It is an exact integer; and so is 16.

If you measure the side of a square and use it to calculate the area, then the uncertainty in the area is determined by the uncertainty in the original measurement or the side.

In any physics experiment, you would always estimate the uncertainty in that original measurement, and express it as, for example, 4.0 ±0.1m; or even 4.000 ±0.001m if you can measure to 1mm.

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What do you mean "we don't see that in an actual experiment"?

In my first post I wrote

There are 2 different considerations here.

Normally in problem calculations in physics, we are given numbers to put into equations and calculate answers. The general advice given is as you say. Give the answer to the least number of significant figures in the data supplied. The data supplied, on the other hand, should be consistent. The value in your example should (would?) be stated as 4.0m

I then wrote

On the other hand, we also use values measured in experiments to calculate something else using a formula, possibly. Here the treatment is different.

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Stonebridge said:Sorry, I don't understand what you are now asking.

What do you mean "we don't see that in an actual experiment"?

In my first post I wrote

I then wrote

sorry for replying sooooo late

i talked about an example where the uncertainty of a measurement is very small let say the area of a squared box is to be calculated for that let us say that we calculated the length the original measurement is 5m and uncertainty is 0.0005m after adjustment we will get the value of 4.9995 now the number of significant figures is now 5 same goes for the width as the box is squared now if we are to calculate the area of the box we have two quantities in which the minimum number of figures are 5 so can we obtain a result that contains 5 digits (i know that the question is a little complicated and english is not my first language i hope that you will understand thank you )

The formula for finding the area of a square box is length x width. In this case, since the area is given as 16 m² and there is only 1 significant figure, the length and width must be equal, making the side length of the square box 4 meters.

The number of significant figures used when calculating the area of a square box depends on the given information. In this case, since the area is given as 16 m² with only 1 significant figure, the answer should also have 1 significant figure.

The value of the side length of the square box can be found by taking the square root of the area. In this case, the side length is √16 m = 4 m.

You can check your answer by using the formula for finding the area of a square box and plugging in the values for the side length. In this case, the formula would be 4 m x 4 m = 16 m², confirming that the answer is correct.

No, the area of a square box cannot be negative. It is a measure of the space occupied by a square and therefore, must always be a positive value.

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