Transcript Applied Geometry

Geometry
Lesson 1 – 2 Extended
Precision and Accuracy
Objective:
Determine precision of measurements.
Determine accuracy of measurements.
Precision
Precision refers to the clustering of a group
of measurements.

Depends on the smallest unit of measure.
Absolute Error
Absolute error of a measurement is equal to
one-half the smallest unit of measure.
The smaller the unit the more precise the
measurement.
Smallest unit – 1 cm
Absolute error – 0.5 cm
Example
Find the absolute error of each
measurement. Explain its meaning.
6.4 cm
Smallest unit of measure is 0.1 cm or 1 mm
Absolute error is 0.1/2 cm
Absolute error is 0.05 cm
Means that it can be between 6.35 and 6.45 cm
6.4 – 0.5 & 6.4 + 0.5
Example
2 ¼ inches
Smallest unit of measure is ¼ inch.
Absolute error is ¼ / 2 in 1 4 1
1 1 1
 2  * 
2
4
4 2 8
Absolute error is 1/8 in
1 1
2  in
4 8
Means it can be between
1 1
2 
4 8
1
3
2 & 2 in
8
8
1 1
&2 
4 8
Example
Find the absolute error and explain its
meaning.
1 ½ inches
Absolute error: ¼ in
1 1
1 
2 4
1
3
between 1 & 1
4
4
Example
Find the absolute error and explain its
meaning.
4 centimeters
Absolute error: 0.5 centimeters
(use decimal for metric)
4 + 0.5 cm
Between 3.5 & 4.5 cm
Significant digits
Precision in a measurement is usually
expressed by the number of significant
digits reported.
Significant digits
Nonzero digits are always significant
In whole numbers, zeros are significant if
they fall between nonzero digits.
In decimal numbers greater than or equal to
1, every digit is significant.
In decimal numbers less than 1, the first
nonzero digit and every digit to the right are
significant.
Determine the number of significant digits.
779,000 mi
3 significant digits
Look at rule for whole numbers.
50,008 ft
5 significant digits
Look at rule for whole numbers
430.008 m
6 significant digits
Look at rule of decimals > 1
0.00750 cm
3 significant digits
Look at rule of decimals < 1
230.004500
9 significant digits
Look at rule of decimals > 1
Accuracy
Refers to how close a measured value
comes to the actual or desired value.
Accuracy vs. Precision
Accurate, but
not precise
Not accurate
& not precise
Precise, but
not accurate
Accurate
& precise
Relative Error
Relative error is the ratio of the absolute
error to the expected measure.
absolute error
exp ected measure
Find Relative error
A manufacturer measures each part for
a piece of equipment to be 23 cm in
length. Find the relative error of this
measurement.
0.5 cm
 0.022 or 2.2%
23 cm
Find the relative error
3.2 mi
0.05 mi
 0.0156  1.6%
3.2 mi
1 ft
0.5 ft
 0.5  50%
1 ft
26 ft
0.5 ft
 0.01923  1.9%
26 ft
Homework
Pg. 24 1 – 23 all