Prentice Hall Geometry

Skills Handbook > The Effect of Measurement Errors on Calculations

The Effect of Measurement Errors on Calculations

Measurements are always approximate, and calculations with these measurements produce error. Percent error is a measure of accuracy of a measurement or calculation. It is the ratio of the greatest possible error to the measurement.

percenterror . equals . fraction greatestpossibleerror , over measurement end fraction

Example

The dimensions of a box are measured as 18 in., 12 in., and 9 in. What is the percent error in calculating the box's volume?

The measurements are to the nearest inch, so the greatest possible error is 0.5 in.

Volume:

as measured	maximum value	minimum value
V = ℓ ⋅ w ⋅ h = 18 ⋅ 12 ⋅ 9 = 1944 in . 3 table with 3 rows and 3 columns , row1 column 1 , v , column 2 equals , column 3 script l dot w dot h , row2 column 1 , , column 2 equals , column 3 18 dot 12 dot 9 , row3 column 1 , , column 2 equals , column 3 1944 , in , . cubed , end table	V = ℓ ⋅ w ⋅ h = 18.5 ⋅ 12.5 ⋅ 9.5 ≈ 2196.9 in . 3 table with 3 rows and 3 columns , row1 column 1 , v , column 2 equals , column 3 script l dot w dot h , row2 column 1 , , column 2 equals , column 3 18.5 , dot , 12.5 , dot 9.5 , row3 column 1 , , column 2 almost equal to , column 3 2196.9 , in , . cubed , end table	V = ℓ ⋅ w ⋅ h = 17.5 ⋅ 11.5 ⋅ 8.5 ≈ 1710.6 in . 3 table with 3 rows and 3 columns , row1 column 1 , v , column 2 equals , column 3 script l dot w dot h , row2 column 1 , , column 2 equals , column 3 17.5 , dot , 11.5 , dot 8.5 , row3 column 1 , , column 2 almost equal to , column 3 1710.6 , in , . cubed , end table

Possible Error:

maximumvalue . minus , measured	measured , minus . minimumvalue
2196.9 , minus , 1944 , equals , 252.9	1944 , minus , 1710.6 , equals , 233.4
percent error = greatest possible error measurement = 252.9 1944 ≈ 0.1300926 table with 3 rows and 2 columns , row1 column 1 , percenterror , column 2 equals . fraction greatestpossibleerror , over measurement end fraction , row2 column 1 , , column 2 equals . 252.9 over 1944 , row3 column 1 , , column 2 almost equal to . 0.1300926 , end table

The percent error is about 13%.

Exercises

Find the percent error in calculating the volume of each box given its dimensions. Round to the nearest percent.

10 cm by 5 cm by 20 cm
1.2 mm by 5.7 mm by 2.0 mm
1.24 cm by 4.45 cm by 5.58 cm
8 , and 1 fourth in. by 17 1 12 in. 17 , and 1 twelfth , in. by 5 in.

Find the percent error in calculating the perimeter of each figure.

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The Effect of Measurement Errors on Calculations

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