Measure the area of the rectangular box with length of 11.5 cm (plus or minus) 0.1 cm, and a height of 1 cm(plus or minus) 0.1 cm. Use a two-repetition approach: the highest and lowest possible bounds. The standard or accepted value is 9.80 cm^2. Give the percent relative and absolute errors. Discuss the sources of these errors. Which dimension contributes greatest to the relative error?
Absolute error = | Observed value – Expected value |.
Relative error = (Observed value – Expected value)/ Expected value.
Relative absolute error = | Observed value – Expected value |/ Expected value.
Percent relative error = (Observed value – Expected value)/ Expected value × 100%.
The length is given as (11.5 ± 0.1) cm.
So, the absolute error for length is 0.1 cm.
Relative error percentage
= (0.1/11.5) × 100%
So, the percent relative absolute error for length is 0.87%.
The height is given as (1 ± 0.1) cm.
So, the absolute error for height is 0.1 cm.
Relative error percentage
= (0.1/1) × 100%
So, the percent relative absolute error for height is 10%.
Lowest possible bound of length = (11.5 – 0.1) cm = 11.4 cm.
Highest possible bound of length = (11.5 + 0.1) cm = 11.6 cm.
Lowest possible bound of height = (1 – 0.1) cm = 0.9 cm.
Highest possible bound of height = (1 + 0.1) cm = 1.1 cm.
Thus, lowest possible bound of area = (11.4 × 0.9) cm = 10.26 cm.
Highest possible bound of area = (11.6 × 1.1) cm = 12.76 cm.
The standard or expected value of area = 9.8 cm2.
With respect to the lowest possible bound of area, absolute error = (10.26 – 9.8) cm = 0.46 cm.
So, the absolute error for area with respect to the lowest possible bound of area is...
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