Understanding Uncertainty in Dimensional Analysis

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To calculate the area of a rectangular plate with dimensions of 23.2 cm (length) and 9.0 cm (width), the area is initially estimated as 208.88 cm². The uncertainties in the measurements are 0.2 cm for length and 0.1 cm for width, which must be factored into the area calculation. The maximum area, considering these uncertainties, is found by adding the uncertainties to the dimensions, resulting in an area of approximately 209.48 cm², while the minimum area is about 208.28 cm². This range illustrates the uncertainty in the area calculation, emphasizing the importance of understanding how measurement uncertainties affect final results. The discussion highlights the method to derive the area and its uncertainty from the given dimensions.
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IM not even sure how to go about solving this problem, but its due Monday morning

rectangular plate has a length of 23.2 +/- .2 cm and a width of 9.0 +/- .1 cm. calculate the area and its uncertainty...
 
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Well, what would you do to start? Suppose someone just came up to you and said, "I've got a rectangular plate here in my bag, and it's around 23.2 cm by about 9 cm." What would you estimate the area to be?

Once you have that, how far could you be off from the real answer, given the uncertainties stated in the problem? In other words, what the largest area that could be correct, given those uncertainties, and what's the smallest area that could be correct? The difference shows you the uncertainty in the answer.

If you can answer those questions, then you can probably see how to get the uncertainty in the answer from the given uncertainties in the provided information.
 
Let's start with the length of the plate. When you say the length is 23.2 +/- 0.2 cm, what does that mean physically?
 

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