Transcript Measurements, Accuracy and Precision, and SigFigs

MEASUREMENTS AND CALCULATIONS
IN CHEMISTRY
Accuracy Vs. Precision
Measuring and obtaining data experimentally always
comes with some degree of error.
Human or method errors & limits of the instruments
We want BOTH accuracy AND precision
EXPERIMENTAL ERROR
Selecting the right piece of equipment is key
Beaker, Graduated Cylinder, Buret?
Measuring 1.5 grams with a balance that only reads
to the nearest whole gram would introduce a very
large error.
ACCURACY
So what is Accuracy?
Accuracy of a measurement is how close the
measurement is to the TRUE value
“bull’s-eye”
ACCURACY
An experiment calls for 36.4 mL to be added
Trial 1: delivers 36.1 mL
Trial 2: delivers 36.6 mL
Which is more accurate???
Trial 2 is closer to the actual value (bull’s-eye),
therefore it is more accurate that the first delivery
PRECISION
Now, what about Precision??
Precision is the exactness of a measurement.
It refers to how closely several measurements of the same
quantity made in the same way agree with one another.
“grouping”
ERROR
Maximizing Accuracy and Precision will help to
Minimize ERROR
Error is a measure of all possible “mistakes” or
imperfections in our lab data
As we discussed, they can be caused from us (human
error), faulty instruments (instrumental error), or from
simply selecting the wrong piece of equipment
(methodical error)
ERROR
Error can be calculated using an “Accepted Value” and
comparing it to the “Experimental Value”
• The Accepted Value is the correct value based on
reliable resources (research, textbooks, peers, internet)
• The Experimental Value is the value YOU measure in
lab. It is not always going to match the Accepted
value… Why not??
ERROR
Error is measured as a percent, just as your grades on a
test.
Percent Error = accepted – experimental
accepted
x100%
• This can be remembered as the “BLT” equation:
bigger minus littler over the true value 
SIGNIFICANT FIGURES
Significant Figures (SigFigs) of a
measurement or a calculation consist of all
the digits known with certainty as well as one
estimated, or uncertain, digit
ALWAYS ESTIMATE one more digit when
reading measurements!!
Homework:
“Reading instruments” practice
RULES FOR DETERMINING
SIGFIGS
1. Nonzero digits are always significant
2. Zeros between nonzero digits are significant
3. Zeros in front of nonzero digits are NOT
significant
4. Zeros both at the end of a number and to the
right of a decimal point ARE significant
5. Zeros at the end of a number but to the left of a
decimal point may or may not be significant
SIGFIGS
5. Zeros at the end of a number but to the left of a
decimal point may or may not be significant
If a zero has not been measured or estimated, it is
NOT significant. A decimal point placed after zeros
indicates that the zeros are significant.
i.e. 2000 m has one sigfig, 2000. m has four
PRACTICE WITH SIGFIGS
How many sigfigs do the following values have?
46.3 lbs
40.7 in.
580 mi
87,009 km
0.009587 m
580. cm
0.0009 kg
85.00 L
580.0 cm
9.070000 cm
400. L
580.000 cm
CALC WARNING
Calculators DO NOT present values in the proper
number of sigfigs!
Exact Values have unlimited sigfigs
Counted values, conversion factors, constants
CALCULATING WITH SIGFIGS
Multiplying / Dividing
The answer cannot have more sigfigs than the value
with the smallest number of original sigfigs
ex:
12.548 x 1.28 = 16.06144
This value only has 3 sigfis, therefore the
final answer must ONLY have 3 sigfigs!
CALCULATING WITH SIGFIGS
Multiplying / Dividing
The answer cannot have more sigfigs than the value
with the smallest number of original sigfigs
ex:
12.548 x 1.28 = 16.06144
= 16.1
This value only has 3 sigfis, therefore the
final answer must ONLY have 3 sigfigs!
PRACTICE
How many sigfigs with the following FINAL
answers have? Do not calculate.
12.85 * 0.00125
4,005 * 4000
48.12 / 11.2
4000. / 4000.0
CALCULATING WITH SIGFIGS
Adding / Subtracting
The result can be NO MORE certain than the least
certain number in the calculation (total number)
ex:
12.4
18.387
+ 254.0248
284.8118
The least certain number is only certain to the “tenths” place.
Therefore, the final answer can only go out one past the decimal.
CALCULATING WITH SIGFIGS
Adding / Subtracting
The result can be NO MORE certain than the least
certain number in the calculation (total number)
Least certain number (total number)
ex:
12.4
18.387
+ 254.0248
284.8118 =
284.8
The least certain number is only certain to the “tenths” place.
Therefore, the final answer can only go out one past the decimal.
CALCULATING WITH SIGFIGS
Both addition / subtraction and multiplication /
division
Round using the rules after each operation.
Ex: (12.8 + 10.148) * 2.2 =
22.9 * 2.2 = 50.38 = 50.
SCIENTIFIC NOTATION
• Scientific Notation – a number written as the
product of two values:
• A number out front &
• A
x10 to a power
• This notation allows us to easily work with very,
very large numbers or very, very small numbers.
SCIENTIFIC NOTATION
• The number out front MUST be written with
ONLY one value prior to the decimal point
Examples:
a. 3.24x104g
= 32,400 grams
b. 2.5x107mL
= 25,000,000 mL
SCIENTIFIC NOTATION
• The exponent (x104) value can have a power that is
positive or negative, depending on if you are dealing
with a SMALL number or a LARGE number
Examples:
a. 8.55x104g
= 85,500 grams
b. 4.67x10-4 L
= 0.000467 Liters
SCIENTIFIC NOTATION
Addition / Subtraction
6.2 x 104 + 7.2 x 103
SCIENTIFIC NOTATION
Addition / Subtraction
6.2 x 104 + 7.2 x 103
First, make exponents the same
62 x 103 + 7.2 x 103
Do the math and put back in Scientific Notation
SCIENTIFIC NOTATION
Multiplication / Division
3.1 x 103 * 5.01 x 104
The “mantissas” are multiplied and the exponents
are added.
(3.1 * 5.01) x 103+4
16 x 107 = 1.6 x 108
Do the math and put back in Scientific Notation
(with correct number of sigfigs)
Homework:
SigFigs Worksheet