1.07 Accuracy
and Precision
Concepts
Standards & Objectives
Standards:
• MA.912.S.1.2—Determine appropriate and
consistent standards of measurement for
the data to be collected in a survey or
experiment.
Objectives:
• Distinguish between Accuracy and Precision
• Determine the number of significant figures in a
measurement.
• Read and record measurements with the correct
number of significant figures.
Key Word
Definition
Example
Accuracy
the closeness of a
measurement to the true
or accepted value
Hitting the Bullseye on
the dartboard
Precision
agreement among a set
of measurements made
of the same quantity in
the same way.
Hitting the same spot
with darts the same time.
(repeatability or
consistency)
Identify the following as accurate or precise.
1.
2.
3.
1. Not accurate or precise.
2. Accurate and precise
3. Precise but not accurate.
*Same spot but not on the bullseye
Accuracy and Precision
Carpenter 1
Carpenter 2
Measurement 1
47.5 cm
Measurement 1
47.0 cm
Measurement 2
46.8 cm
Measurement 2
47.1 cm
Measurement 3
45.3 cm
Measurement 3
46.9 cm
If the window measures 47 cm exactly
Are the measurements accurate/precise?
Accuracy and Precision
Carpenter 1
Carpenter 2
Measurement 1
47.5 cm
Measurement 1
47.0 cm
Measurement 2
46.8 cm
Measurement 2
47.1 cm
Measurement 3
45.3 cm
Measurement 3
46.9 cm
If the window measures 47 cm exactly
Are the measurements accurate/precise?
Carpenter 1: has measurement’s with great variety.
Neither accurate or precise.
Carpenter 2: precise, accurate if the true length is
around 47.0 cm.
Significant Figures
• Suppose you were asked to measure the
length of a pencil using a ruler in cm?
• How do you measure accurately and
precisely?
Why use Significant Figures?
• I might say 6.7, you might say 6.8, your
friend might say 6.75 cm. Who is right?
How do we show consistency in the way all
scientists read and record measurements?
Significant Figures
Keyword
Definition
Example
Significant Figure
All digits in a
See Rules for significant
measurement that are
figure examples.
known with certainty plus
one final digit that is
estimated and uncertain.
Graduation
A line that marks a
measurement, (dash
marks on a rule or
graduated cylinder)
Example below
What is a Sig Fig?
• Use significant figures (sig figs for short) in
3 ways:
1. You will make measurements and report them
to others. Determine the number of sig figs by
estimating one digit past the smallest measurement, or
graduation, on the measuring tool.
What is a Sig Fig?
Ex. 1: The graduations go in 10 degree increments. So, you can know the
temperature for certain to the tens place and can estimate in the ones
place. Estimate that the temperature is 6°C, 7°C, 8°.
Ex. 2: The graduations on this thermometer mark off every one degree.
You can measure the temperature to the ones place for certain and can
estimate to the tenths place. You may read this thermometer as 3.6°C,
3.7°C, 3.8°.
Ex 3: The graduations on this thermometer mark off every tenth of a
degree (o.1 increments). You can know the temperature to the tenths
place for certain and can estimate to the hundredths place. You may
have read this temperature as 0.69°C, 0.70°C, 0.71°.
What is a Sig Fig?
2. You will interpret the measurements reported
by others. Data provided will show the instrument
used because you know that scientists always estimate
one digit past the smallest graduation on a measuring
tool.
3. You will need to keep track of sig figs when
measurements are used in calculations. You
must have correct values in measurement to use
correct # of sig figs in calculations.
Rules to Determine Sig Figs
Significant Figures
Example
22.51 g
0.076 g
200 mL
250.0 mL
2.20 x 10^-3 g
Answer
Explanation
Significant Figures
Example
Answer
Explanation
22.51 g
4 Sig Figs
Rule 1 All nonzero
numbers are significant
0.076 g
2 Sig Figs
Rule 3 Zero’s to the left
are not significant
200 mL
1 Sig Fig
Rule 4 Zero’s at the end
only count of there is a
decimal
250.0 mL
4 Sig Figs
Rule 4 Zero’s at the end
count only if there is a
decimal
2.20 x 10^-3 g
3 Sig Figs
Rule 5 all digits of a
coefficient in scientific
notation count .
Sig Figs in Calculations
• The results of the calculations are not
allowed to appear more or less accurate
than the original measurements used.
• Follow simple rules when multiplying,
dividing, adding, or subtracting helps make
sure that all results are represented with
the appropriate amount of reliability.
Rules for Multiplication/Division
• Only given measurements affect the number of sig figs
allowed in the final answer. Conversion factors or equivalences
don’t affect it. (Ex: 1 m= 1000 mm)
• If you are only given one measurement, the total number
of sig figs in that measurement equal the total number of
sig figs allowed in your final answer.
• If you are given more than one measurement, the final
answer must be rounded to the same total number of sig
figs as the measurement that has the least.
Rules for Multiplication/Division
Example problems
1. Convert 72.0 cm to the unit dam.
2. Calculate the density of an object that has a
mass of 104.5 g and a volume of 64.0 mL.
Rules for Multiplication/Division
Example problems
1. Convert 72.0 cm to the unit dam.
72.0 cm
10^-2 m
1 dam
= 0.0720 dam
1 cm
10^1 m
2. Calculate the density of an object that has a
mass of 104.5 g and a volume of 64.0 mL.
D = mass / volume
Density = 104.5 g / 64.0 mL
Density = 1.6328 g / mL
**Round to 3 sig figs b/c 64.0 mL only has 3
Final answer 1.63 g /mL
Rules for Addition/Subtraction
• The final answer cannot have more places
after the decimal than any of the given
measurements.
• The final answer cannot have a final digit,
which represents the uncertain or
estimated place, farther to the right than
any of the final digits in the measurements
used.
Rules for Addition/Subtraction
Example problems
1. Add 101.5g + 17.86 g
1. Subtract 101.5g - 17.86 g
Rules for Addition/Subtraction
Example problems
1. Add 101.5g + 17.86 g
= 28.36 g
Actual answer w/ correct Sig Figs can only have 1
place after decimal.
28.4 g
2. Subtract 101.5g - 17.86 g
83.64 g , Actual answer can only have 1 place
after decimal
83.6 g
Rules for Rounding up or down
• It is sometimes necessary to round your
answer or add zeros to the end of the
answer to give it the proper number of sig
figs.
Rules for Rounding up or down
Example problems
1. Calculate the density of an object that has a mass of
101.3 g and a volume of 49.5 mL.
Density = mass/ volume
Density = 101.3 g / 49.5 mL
Density = 2.046 g/mL
Final answer can only have 1 place after decimal and no more than 3 sig figs,
whatever is less. Round down.
** 2.0 g/mL
2. If a beaker containing a sample of powder has a mass
of 65.09 and the clean, empty beaker has a mass of
54.69 grams, what is the mass of the powder?
65.09 – 54.69 g = 10.4 g but must round to 2 decimals places after decimal,
so add a zero.
**10.40 g
Practice with Estimating Sig Figs
Practice with Estimating Sig Figs
89.9 mL
27.79 mL
54 mL
Practice with Estimating Sig Figs
Practice with Estimating Sig Figs
55.8 mL
32.81
mL
45 mL
What’s next? The Virtual Lab
Lab worksheet link: https://sites.google.com/site/chemistryflvs/Tutorials/labreport-files/1_07AccuracyandPrecisionLabWorksheet.doc?attredirects=0&d=1
or go to the Chemistry Resource Center and click Blank Lab reports.