Precision vs. Accuracy
There really is a difference
Accuracy
• Accuracy is how close the measured
value is to the true or actual amount
or answer.
Precision
• How close the measurements are to
each other
• How many decimal places are in the
measurement.
Precision or Accuracy?
Which measurement is most
precise?
• 0.01 m
• 0.005 m
• 0.0053 m
Significant Figures
Where do I round the answer? How do I
record this measurement?
Significant Figures
• Significant figures are important to
measurements
• All nonzero digits are significant
• Ex. 852 cm has 3 sig figs
When Zeros
are Sig Figs
• Zeros are significant when they are
between nonzero digits (sandwich
rule) ex. 700,001 g
• Zeros are significant when it comes
after a decimal point and a nonzero
digit. (Power of Two Rule)
• Ex. 1.00 cm
When zeros are
NOT sig figs
• If the zeros come before a nonzero
digit
ex. 0.00007346 m
• If it is at the end of a number that
does NOT have a decimal point
ex. 18,000,000 g
When Sig Figs
are Infinite
• All Conversion Factors and Counting
numbers have INFINITE significant
figures
• Ex. 2.54 cm = 1 inch (both the 2.54 and the
1 are infinitely significant)
• Counted values contain infinite significant
• Ex. You have 1 science book on your desk.
That 1 has infinite sig figs because it is
known to have been counted not measured.
Summary of Sig Figs
• Nonzero digits are always significant
• Zeros are significant if they are between
two non zero digits or if there is BOTH a
decimal and a nonzero digit in front of the
zeros
• Zeros are NOT significant in other
situations (just a decimal, after a number
without a decimal)
Sig Figs in
Measurement
How to record the correct
measurement
Significant Figures
• Read the correct
number of
significant figures
Measure the following using
significant figures
Use Sig. Figs to find this
measurement
Use the correct number of
sig. figs in this
measurement
What digit would be
estimated in using this
ruler?
A.
B.
C.
D.
E.
Ones
Tenths
Hundredths
Thousandths
Tens
What decimal place is
estimated when using
this ruler?
A. Ones
B. Tenths
C. Hundredths
D. Thousandths
E. Tens
Measure the width of the
rectangle using the correct
number of sig figs.
A. 3. 75 cm
B. 3.6 cm
C. 2. 6 cm
D. 3.60 cm
E. 4.25 cm
Measure the length of the
rectangle using the correct
number of sig figs.
A. 12.55 cm
B. 12. 5 cm
C. 12.0 cm
D. 13.50 cm
E. 13. 5 cm
How many sig figs should be in
the correct measurement of
the length of this rectangle?
A. 2 sig figs
sig fig
B. 3 sig figs
C. 4 sig figs
D. 5 sig figs
E. 1
The width of this rectangle is 0.90
cm. How many significant figures
are in this measurement?
A. 3 sig figs
B. 2 sig figs
C. 1 sig fig
D. infinite sig figs
E. none of the above
QOD—Entrance Ticket
What is the mass to the correct
number of significant digits?
QOD—Record the mass on this balance to
the correct number of significant digits
and record the unit of measure.
Calculations with
Significant Figures
Multiplication and Division
Addition and Subtraction
Multiplication and
Division
• When multiplying and dividing the
answer is rounded to the LEAST
number of sig figs of the data used
in the calculations
• Examples to follow
Example 1
Ex. 9.00 cm x 1,000 cm =
9.00 cm = ______ sig figs
9.00 cm = 3 sig fig (decimal and 9)
1,000 cm = _______ sig figs
1,000 cm = 1 sig fig (no decimal just a 1)
Least number of sig figs?
1 sig fig, so answer should have only one sig fig as
well.
9,000 cm2 (1 sig fig zeros are not significant; only a
9 but no decimal)
Example 2
Ex. 78.0034 g / 80.0 mL =
78.0034 g = ____ sig figs
78.0034 g = 6 sig figs (sandwich rule)
80.0 mL = ___ sig figs
80.0 mL = 3 sig fig (8 and decimal)
Least number of sig figs?
3 sig figs so answer should have 3 sig figs
Calculator answer = 0.9750425 round to 3 sig figs
0.975 g/mL is the final, rounded answer
Example 3
Ex. 9.70 x 104 m x 1.76 x10-2 m
9.70 x 104 m = ___ sig figs
9.70 x 104 m = 3 sig figs (decimal and non zero
digits)
1.76 x10-2 m = ____ sig figs
1.76 x10-2 m = 3 sig figs (all non zero digits)
Which is the least number of sig figs?
Both are the same, so there will be 3 sig figs in
the answer.
Calculator says = 1707.2 m2
Rounded to 3 sig figs may look like this 1710 m2
or in scientific notation it would be 1.71 x 103
m3
Either answer is acceptable unless the
directions state the answer must be in
scientific notation.
Addition and Subtraction
with Sig Figs
• The least number of decimal places in
the input is the same number of
decimal places in the output (answer).
Example 1
• 12.573 m + 3847.91 m – 378.1 m = ?
• What is the LEAST number of
decimal places?
• One decimal place, so the answer
should have one decimal place
• 3482.383m (un-rounded)
• 3482.4 m (rounded)
Try these in your notes
1. A rectangle has a width of 5.00 cm
and a length of 8.40 cm. What is
the area of this rectangle in cm2?
___________
Answer
• Calculator says 42
• But we need 3 sig figs and this is only
2. What should we do?
• 42.0 cm2 or 4.20 x 101 cm2
Try this one in your
notes
2. A triangle has the following
measurements: side A 8.54 cm, side
B 7.8cm, and side C 10.000 cm.
What is the perimeter in cm?
______________
Answer
• Calculator displays 26.34
• We need only1 decimal place, so what
should we do?
• 26.3 cm Did you remember the unit
of measurement in your answer?
Summary
• Multiplication and Division use the least
number of significant figures in the data
to round to that number of sig figs in the
answer.
• Addition and Subtraction use the least
number of DECIMALS in the data to round
to that number of DECIMALS in the
answer
• Don’t forget your unit of measurement