Transcript Data Recording and Significant Figures

Data Recording and Significant
Figures
Data Recording and
Significant Figures
Accuracy and Precision
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Accuracy
• How close a
measurement is to
the accepted value
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Precision
• repeatability in
measurements.
• The number of
decimal places. For
example: 0.1g has
less precision than
0.100g.
Recording measurements off of
equipment.
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estimate one more digit than the
equipment provides.
Recording measurements
continued
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Exception: with electronic
equipment, the user is rounding off
digits rather than adding them. For
example, 2.3456g will be
rounded to 2.35g.
Round to nearest .001g.
Using uncertainty in measurements
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The estimated digit used when recording
data can be written with an uncertainty
notation, ± in the measurement.
Example; a graduated cylinder that
measures to the nearest ml is used for
volume measurements. A student
measures 3 different volumes using the
same cylinder: 15.5ml, 15.8ml, 15.2ml in
an experiment. How would one record
these measurements using uncertainty?
Significant Figures

What are significant figures?
• They are digits in measurements that
were actually measured or estimated in
some way.
• Numbers that are not measurements
are not considered to be significant
figures.
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Examples are 100 in percent equations, pi,
and constants used in scientific equations
Rules for using zeros.
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Rule 1: Leading zeros are not
significant. These are zeros which
precede digits in decimal numbers.
• Examples: 0.045g., 0.23
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Rule 2: Captive zeros are significant.
These are any zeros that are in
between non zero numbers.
• Example 2,013, 0.0101, 100.01
Use of zeros continued
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Rule 3: Trailing zeros are not
significant. These are zeros at the
end of large numbers with no
decimal point.
• Examples: 100, 10, 2,340 35,000
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Scientific notation is used to remove
the trailing zeros. Example: 35,000
becomes 3.50 x 104
Rules for rounding off
measurements
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Rule 1: when reducing the number of
digits, look at the first digit that must
be eliminated.
• If it ends in a number greater than 5
round up.
• If it ends in a number less than 5 round
down.
• If it ends exactly in 5, round to the
nearest even number.
Rules for rounding in calculations
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Addition and subtraction
• Round off the final answer to the same
number of decimal places as the
measurement with the fewest decimal
places.
• Examples. 2.34g + 2.4g + 2.35g=7.09g
this should be rounded to 7.1g
Rounding continued
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Multiplication and division
• The final answer has the same number
of significant figures as the
measurement with the fewest significant
figures.
• Example 150.ml x 2.0 x 4.14 = 1242
this must be rounded off to :
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1.2x 103