6th Grade Math Textbook, Fundamentals

Find the absolute error and the relative error for Nancy’s measurements.

Use your results to explain which measurement is more accurate.

So the measurement on the second scale is more accurate

because it has the smaller relative error.

actual weightmeasurementabsolute error given measurementGPE relative error

67.2 oz 64 oz 3.2 oz 0.125 12.5%

0.5 lb

4 lb

67.2 oz 67 oz 0.2 oz 0.007 0.7%

0.5 oz

67 oz

First

Scale

Second

Scale

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Lesson 10-1 for exercise sets. &KDSWHU 

1.Identify the unit of precision for the ruler shown on page 272.

Give the GPE and the percent of relative error to the nearest tenth of a percent.

2.72 ft 3.14 oz 4.12.5 mm

5.Discuss and Write If you measure the width of a rectangle as 4.55 cm and you

measure its length as 8.4 cm, how would you express its area? Explain.

1

Measurements obtained experimentally (by using a ruler or other measuring

instrument) should be stated with a number of significant digits, which give a

reasonable impression of the precision of the measurement.

are all nonzero digits, zeros between nonzero digits, and zeros following the last

nonzero digit to the right of the decimal point. For example, 85,401has five

significant digits, and 0.050has twosignificant digits.

When adding or subtracting experimental measurements, round the final result

to have the same number of decimal places to the right of the decimal point as the

measurement that has the fewest decimal places to the right of the decimal point.

When multiplying or dividing experimental measurements, round the final result

to have the same number of significant digits as the measurement that has the

fewest significant digits.

Significant digits

Key Concept

Absolute Error and Relative Error

• No measurement is exact. The uncertainty in any given measurement is
  referred to as error. The error does notmean “mistake.”


• The of a measurement is the actual size of the error.
  It can be represented by the GPE.


• The of a measurement is the absolute error in relation to the
  correct value (or to the measured value if the correct value is not known).

relative error

absolute error