Transcript Accuracy & Precision & Significant Digits

Accuracy & Precision
&
Significant Digits
Accuracy & Precision
 What’s difference?
 Accuracy – The closeness of the
average of a set of measurements to the
true value.
 Ex. Density of Hg = 13.6 g/mL
 Trials – 13.6, 13.0, 14.2 g/mL
Accuracy & Precision
 Precision – The closeness of the values
of a set of measurements to each other.
 Ex. Density of Hg = 13.6 g/mL
 Trials – 13.1, 13.0, 12.9 g/mL
 The true value does not matter in being
precise.
Target Practice
Accurate & Precise
Target Practice
Accurate, not Precise
Target Practice
Precise, not Accurate
Target Practice
Not Accurate or Precise
Accuracy & Precision
 Experimental error – the lack of ability to
measure anything to an exact value.
 Error is not a mistake, but a lack of
certainty in the measurements.
 This leads to...
Significant Digits
(or Significant Figures)
 Every digit in a measurement reflects the
accuracy of that measurement.
 All the digits are known with certainty with
the final digit being estimated.
 <<ADD MEASUREMENT OH>>
Triple Beam Balance
Volume Readings
Rules for Determining
Significant Digits
 1) Non-zero digits are always significant.
 3.25 m
 867.14 cm
 19 km
Rules for Determining
Significant Digits
 2) Any zeros between non-zero digits are
always significant.
 3005 g
 870004 mm
 101 m
Rules for Determining
Significant Digits
 3) Any zeros to the left of all non-zero
digits are NOT significant.
 0.042 kg
 0.00003 m
 0.000000000000000000000155 g
Rules for Determining
Significant Digits
 4) Final zeros (zeros to the right of the
last non-zero digit) with a decimal point
are significant.
 2.000 g
 400 cm
 400. cm
 0.001200 m
Rules for Determining
Significant Digits
 5) In scientific notation, all of the
coefficient digits are significant.
 1.74 x 109 m
 1.523 x 10-23 g
Rules for Determining
Significant Digits
 6) Numbers that are defined (exact
measurements) do NOT limit the
significant figures in a calculation.
 1.00 m = 100 cm
Practice Sig Digits
 Determine the number of sig. digits in the
following values.
1) 750
6) 0.075
2) 750.
7) 0.00075
3) 750.0
8) 7.500
4) 7005
9) 75.000
5) 755
10)7.5 x 103
Math with Sig Digs
 Addition and Subtraction
 The placement of the last significant digit
in your answer is based on the
measurement with the least amount of
precision.
Math with Sig Digs
 Addition and Subtraction
Ex)
3.95 g
12.879 g
+
214.5
g
231.329 g
231.3
g
Math with Sig Digs
Ex)
13.95
g
−
4.513
g
9.437
g
9.44
g
Math with Sig Digs
 Multiplication & Division
 The number of sig. digits in the
measurement with the fewest sig. digits
determines the number of sig. digits in
your answer.
Math with Sig Digs
 Multiplication & Division
Ex) 2.0 cm x 12.08 cm
2.0 cm x 12.08 cm = 24.16 cm2
24.16 cm2  24 cm2
Math with Sig Digs
 Multiplication & Division
Ex) 4.52 g / 3.533 mL
= 1.2794 g/mL
= 1.28 g/mL
Practice with Math and Sig.
Digits
 Correctly answer the following using proper
significant digits.
1)3.89 m + 12.4 m
2)52 g – 18.240 g
3)1.405 cm x 18.60 cm x 0.0950 cm
4)42.0 g / 20.05 mL
Scientific Notation
 1.23 x 109
 1.23  coefficient
 10  base
 9  exponent
Changing from Sci. Notation
to Decimal Form
 Move the decimal to the left or right the same
number of places as the exponent
 Positive – move to the right 
 Negative – move to the left 
 1.23 x 109
 1.23 x 10-5
Changing from Decimal Form
to Sci. Notation
 Count the number of time the decimal place is
moved to get a number between 1.0 and 9.9.
 The number of moves is your exponent
 Original number > 10, positive exponent
 Original number < 1, negative exponent
 4,200,000
 0.000574