the volume of the rectangular block in the figure is calculated from the following measurements of its dimensions: a = 10.00 ± 0.10 cm, b = 5.00 ± 0.06 cm and c = 4.00 ± 0.04 cm. calculate the error in the value of the volume of the block assuming: a) the errors are independent b) the errors are correlated such that they all push the estimate in the same direction.

The following data sets are the length measurements of a raw material. The actual length of the part is supposed to be 3.2 mm. Which sets) do you prefer to the others? Briefly explain.HINT: Check the accuracy and the precision of each data set.Data Set 1: 2.91, 3.00, 3.50, 2.85, 3.22, 3.15, 3.49, 2.90, 3.27, 3.15Data Set I1: 3.13, 3.22, 3.19, 4.17, 3.21, 2.62, 3.25, 2.80, 2.40, 3.81Data Set I: 3.24. 3.18. 3.22. 3.20. 3.17, 3.23, 3.19, 3.20, 3.16, 3.24Data Set IV: 2.90. 3.00. 2.92. 2.95. 2.93. 2.97. 2.94. 2.99. 2.96, 3.00     Please donot provide solution in image format and it should be in step by step format and provide fast solution

(a) How many significant figures are in the numbers 999.0 and 1000.0? 999.01000.0 (b) If the uncertainty in each number is 10, what is the percent uncertainty in each? (Give your answer to 4 significant figures.) 999.0  %1000.0  % (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?

You purchased 5.2kg of apples from a store. You noticed that they used the smallest division of 4.2 g to weight them. What is the relative error of this weight measurement as a percentage. You want to calculate the area of your dorm which is in a rectangular shape. You measure the length and the width of the room as L= 4.8+(-.01) m, W= 4.4+(-.01) m. What is the absolute error in the area in m^2 units?