Transcript Precision and Accuracy

Precision and Accuracy
Uncertainty in Measurements
Precision and Accuracy
Uncertainty

a measurement can only be as good
as the instrument or the method
used to make it.
Ex. Cop’s Radar Gun vs. Car’s Speedometer.
Bank sign Thermometer vs. your skin.
Precision and Accuracy
Accepted Value  A measurement
deemed by scientists to be the “true
measurement.”
Accuracy  The Closeness or proximity of a
measurement to the accepted value.
Precision and Accuracy
Precision  A proven agreement between the
numerical values of a set of measurements
done by the same instrument and/or method.
.
Precision and Accuracy
Significant Figures are the digits used to
represent the precision of a measurement.
SIG. FIGS. are equal to all known
measurements plus one estimated digit.
Rules for Significant Digits
1) ALL NON-ZERO DIGITS ARE SIGNIFICANT
2) EXACT NUMBERS  have an infinite
number of significant numbers.
Exact #s are #s that are defined not measured. Numbers found by
counting or used for conversions such as 100 cm = 1 m.
3) Zeros can be both significant or insignficant
Rules for Significant Digits
The Three Classes of Zeros
A. Leading Zeros  Zeros that precede all
of the non-zero digits are NOT significant.
Ex. 0.0025 mg 
has only 2 sig. figs.( the 2 & 5)
all three zeros are not significant.
Rules for Significant Digits
B. Captive Zeros  Zeros between two or
more nonzero or significant digits ARE
significant.
Ex. 10.08 grams
All four #s are significant
Rules for Significant Digits
C) Trailing Zeros  Zeros located to the
right of a nonzero or significant digit ARE
Significant ONLY if there is a decimal in
the measurement.
Ex. 20.00 lbs  Has four sig. figs.
2000 lbs  Has only 1 sig. figs
Calculations with Significant Digits
Multiplication or Division
The product or quotient must be Rounded so
that it contains the same # of digits as the
least significant measurement in the
problem.
Ex. ( 2.2880 ml )(0.305 g/ml ) = 0.69784 g
Ans. Must be rounded to 3 sig. figs.
mass = 0.698 g
Calculations with Significant Digits
Addition and Subtraction
The sum of two or more measurements must
be rounded to the same number of digits to
the right of the decimal point as the least
precise measurement in the problem.
2.00003 g
EX.
10.234 g
only one digit
+ 333.3 g
=
345.53403 g  345.5 g