Data Recording and Significant Figures

Data Recording and Significant
Data Recording and
Significant Figures
Accuracy and Precision
• How close a
measurement is to
the accepted value
• repeatability in
• The number of
decimal places. For
example: 0.1g has
less precision than
Recording measurements off of
estimate one more digit than the
equipment provides.
Recording measurements
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
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
Examples are 100 in percent equations, pi,
and constants used in scientific equations
Rules for using zeros.
Rule 1: Leading zeros are not
significant. These are zeros which
precede digits in decimal numbers.
• Examples: 0.045g., 0.23
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
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
Scientific notation is used to remove
the trailing zeros. Example: 35,000
becomes 3.50 x 104
Rules for rounding off
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
• If it ends exactly in 5, round to the
nearest even number.
Rules for rounding in calculations
Addition and subtraction
• Round off the final answer to the same
number of decimal places as the
measurement with the fewest decimal
• Examples. 2.34g + 2.4g + 2.35g=7.09g
this should be rounded to 7.1g
Rounding continued
Multiplication and division
• The final answer has the same number
of significant figures as the
measurement with the fewest significant
• Example x 2.0 x 4.14 = 1242
this must be rounded off to :
1.2x 103