With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (a) the area of the rectangle; (b) the ratio of the rectangle’s width to its length; (c) the perimeter of the rectangle; (d) the difference between the length and the width; and (e) the ratio of the length to the width?
Solution 14E The length of the metal piece is l = 12 mm And the width of the metal piece is b = 5.98 mm Step 1 a) The area of the rectangle is 2 A = lb = (12 mm)(5.98 mm) = 71.76 mm Now the length of the metal piece was measured with 2 significant digits and the width was measured with 3 significant digits. Now the area was calculated by multiplying the measurements, and hence the number of significant digits should be the least significant digits of the measured value, which is 2 here. Hence the area should be reported with the 2 significant digits. So the area of the metal piece is 72 mm . Step 2 b) The ratio the rectangle's width to length is r = b= 5.98 m= 0.4983 l 12 mm Now the least significant digit here is 2 and division was done to calculate the ratio, the final result should be reported with two significant digits. Hence the ratio of width to length of the rectangle is 0.50. Step 3 c) The perimeter of the rectangle is L = 2(l + b) = 2(12 mm + 5.98 mm) = 35.96 mm Now the perimeter was calculated with by adding the measurements. During addition we have to report the final result with the minimum precision of the measured values we are adding. In the length measurement the precision is in 1 mm where as in the width measurement the precession is of 0.01 mm. Hence the final result should be reported to the 1 mm precision and hence the above value should be rounded to 1 mm. So the perimeter of the metal piece is 36 mm.