Transcript Accuracy & Precision in Measurement

Accuracy & Precision
in Measurement
Accuracy & Precision
• Accuracy:
• Precision:
• How close you are to the
• How finely tuned your
actual value
• Depends on the person
measuring
• Calculated by the formula:
% Error = (YV – AV) x 100 ÷ AV
measurements are or
how close they can be
to each other
• Depends on the
measuring tool
• Determined by the
number of significant
digits
Where: YV is YOUR measured Value &
AV is the Accepted Value
Accuracy & Precision
• Accuracy & Precision may be demonstrated
by shooting at a target.
• Accuracy is represented by hitting the bulls
eye (the accepted value)
• Precision is represented by a tight grouping
of shots (they are finely tuned)
Accuracy & Precision
Precision without
Accuracy
Accuracy without
Precision
No Precision &
No Accuracy
Accuracy - Calculating % Error
How Close Are You to the Accepted
Value (Bull’s Eye)
Accuracy - Calculating % Error
• If a student measured the room width at
8.46 m and the accepted value was 9.45 m
what was their accuracy?
• Using the formula:
% error = (YV – AV) x 100 ÷ AV
• Where YV is the student’s measured value &
AV is the accepted value
Accuracy - Calculating % Error
• Since YV = 8.46 m, AV = 9.45 m
• % Error = (8.46 m – 9.45 m) x 100 ÷ 9.45 m
•
=
0.99 m
x 100 ÷ 9.45 m
•
=
99 m
÷ 9.45 m
•
=
10.5 %
• Note that the meter unit cancels during the division
& the unit is %. The (-) shows that YV was low
• The student was off by almost 11% & must
remeasure
• Acceptable % error is within 5%
•Acceptable error is +/- 5%
•Values from –5% up to 5% are acceptable
•Values less than –5% or greater than 5% must be remeasured
remeasure -5%
5% remeasure
Significant Digits
How to Check a Measurement for
Precision
Significant Figures
“Sig Figs” are the actual numbers used to
represent a measurement read from an
Instrument.
Numbers that are considered significant are all
of the numbers that can be directly read from
the numbers on an instrument plus one
estimated.
The estimated digit will always be the last
digit.
“IF DOT, THEN RIGHT; IF
NOT THEN LEFT”
Which digits are Significant?
All non-zero (1-9) digits are significant.
Some zeros are Significant, and some are not!
To determine if zeros are significant, use this
simple saying that allows you to draw an arrow to
“cross out” zeroes that are ___NOT________
significant.
The arrow stops when it reaches a nonzero digit.
“IF DOT, THEN RIGHT; IF
NOT THEN LEFT”
How many significant digits are in 0.090?
There is a decimal, so the arrow starts
outside of the number and points to the right.
The first nonzero digit the arrow reaches is a
9, making it, and any digit to the right of it
significant.
Therefore, there are ___two____ sig figs in
0.090.
“IF DOT, THEN RIGHT; IF
NOT THEN LEFT”
How many sig figs are in the number 20400?
There is no decimal, so the arrow starts
outside of the number and points Left.
The first nonzero the digit the arrow reaches
is the 4, making it and any digit to the left of
it significant
Therefore, there are 3 sig figs in the number
20,400
Calculations with Measurements
using Significant Figures
• When adding or subtracting the answer
should be rounded to the fewest decimal
places.
121.34 g + 1.562 g = 122.902 g → 122.90
• When multiplying or dividing, the answer
must have the least number of sig figs.
5.0 m x 6.32 m = 31.6 m → 32 m
Rules For Rounding
Determine the last allowable sig fig based on the
rules and underline it.
• Look at the number directly to the right.
• If that number is LESS than 5, keep the
underlined number the same.
• If that number is GREATER/ EQUAL to 5,
increase the underlined number by 1.
• Use Zeros to keep the place value if necessary
What about the rounding?
When items have been rounded instead of
measured, or for an exactly defined
quantity, there are considered to be an
Infinite number of sig figs
Significant Digits & Precision
•What is the length of the bar?
• How many digits are
there in the
measurement?
• All of these digits are
significant
• There are 3 sig figs.
0
1
2
cm
Length of Bar = 3.23 cm
3
4