I need to make a careful measurement of the size of my rectangular bedroom. I ca
ID: 2133566 • Letter: I
Question
I need to make a careful measurement of the size of my rectangular bedroom. I can use a tape measure to make measurements to a precision of 0.01 m and measure the length to be 4.28 m and the width to be 3.61 m.
With three digits to the right of the decimal point, calculate the perimeter of the room and its absolute uncertainty (same as absolute error)
I got this right w/ perimeter of 15.78 and error of +/- 0.28.
Now calculate the area of the room and its absolute uncertainty (same as absolute error).
Explanation / Answer
From your measurements, length= 4.28+/-0.01.
width= 3.61+/- 0.01.
Now, the area A=(L*W).. A=(3.61*4.28)= 15.4508. This should be rounded off to 15.45. Because your least count is 0.01.
take ln on both sides,
ln A=ln L+ln W.
take derivative on both sides,dA/A = dL/L + dW/W.
so, dA= (15.4508)*(0.01/4.28 + 0.01/3.61) = 0.0789. This also should be rounded off to 0.08.
Therefore, your area = 15.45 +/- 0.08. Without rounding off, your area = 15.4508 +/- 0.0789.