6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-1

Precision and Accuracy

in Measurement

Objective To explore the difference between

precision and accuracy of measurements• To find the

greatest possible error (GPE) and the relative error of a

measurement• To measure to a given unit of precision

• To apply precision and significant digits in computations

Nancy checks the weight of some vegetables. She tries two
different scales in the market. The first scale weighs to the
nearest pound; the second scale weighs to the nearest ounce.
The vegetables weigh 4 pounds on the first scale and 67 ounces

on the second scale. If the vegetables actually weigh 4 pounds,

which measurement is more precise? Which is more accurate?

 refers to the smallest unit of measurement

on the measuring instrument. The smaller the unit of

measurement, the more precise the measurement

will be. So the measurement of 67 ounces is the more

precise measurement.

 refers to how close a measurement is to the

actual value. Since 4 lb 64 oz and 4 lb 67.2 oz, and

since 67 ounces is closer to the actual weight of 67.2 ounces

than 64 ounces is, it is a more accurate measurement than

4 pounds. Note, however, that a more precise measurement

is not alwaysa more accurate measurement.

How long is the key to the nearest centimeter?

To the nearest millimeter?

The key is 3 centimeters or 29 millimeters depending

on the precision of the measurement.

Precision

1

5

1

5

Accuracy

The degree of precision required for a measurement depends

on the situation. A centimeter more or less in the measurement

of a baseball field makes very little difference. A centimeter

more or less in a measurement made by a watchmaker is

very important.

The is considered to be one half of the smallest

unit that the measuring instrument can measure. So, when Nancy measures

the weight of the vegetables as 4 pounds using the first scale, the GPE of her

measurement is pound; and the vegetables could weigh from 3 to 4 pounds.

When Nancy measures the weight of the vegetables as 67 ounces using the

second scale, the GPE of her measurement is ounce; and the vegetables could

weigh from 66 to 67 ounces.

greatest possible error (GPE)

1

2

1

2

1

2

1

2

1

2

1

2

Key Concept

Precision and Accuracy

Measurements are approximate.

The precisionof a measurement

depends on the unit of measure.

The smaller the unit is, the more

precise the measurement is.

The accuracyof a measurement

depends on how close the

measurement is to the exact value.

A measurement is said to be more accurate than another measurement

if its relative erroris smaller.