Name: __________________________
What You’ll Learn



Precision and Accuracy
Uncertainty
Tolerance
Why It’s Important



Working in trades such as construction requires taking many
measurements. To build a good quality and durable home, you have to
be accurate and precise in your measurements.
If you do not take measurement uncertainty into account in a task, you
may find yourself with products that are not the right size for the available
space.
When manufacturing a product, a range of sizes is often acceptable to
allow for error up to a certain limit so that parts will still fit properly.
Key Formulas
Uncertainty =
1
(precision)
2
Tolerance = maximum limit – minimum limit
Grade 12 Essentials – Precision Measurement
Precision and Accuracy: Notes
Accuracy is how
data are to the bull’s eye).
your data points are (i.e. how close your
The accuracy of a measurement is how close it is to the
(also
called the accepted value). If you have measured something accurately,
someone should be able to repeat the same measurement and get the same
value.
Example 1) State the level of accuracy for each scenario.
a) It is accepted that the value of pi is 3.14. You draw a circle, measure its
circumference and diameter, calculate for pi and find that it is 3.19.
b) The speed of light is generally accepted to be 299 792 458 meters per
second. You set up an experiment to test the speed of light and find that
it is 299 795 846 meters per second.
Precision is the
of your data (i.e. how close your data are
to each other) and is determined by the limitations of the measuring instrument.
The precision of a measuring device is the size of the
measurement
on the device. A smaller scale makes it possible to measure with less uncertainty.
Ex. If your measuring device is marked off in centimeters, that is as precise as you
can measure. Your answer will be to the nearest
.A
measurement made with a ruler marked in millimetres would be
precise than a measurement made with a ruler marked in centimetres.
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Grade 12 Essentials – Precision Measurement
NOTE: It is important to know your place values when working with precision.
The smaller the unit, the more precise it is. When reading the precision we read
ONE UNIT in that place value as the precision.
Example 2) What is the precision of the following numbers? Which is more
precise?
a) 45.876
b) 0.56
c) 26
32
d) 8
16
Example 3) State the level of precision for each measuring tape.
3
Grade 12 Essentials – Precision Measurement
Precision and Accuracy: Practice
1. Explain the level of precision needed in each scenario (extreme precision,
moderate precision, and low precision) and suggest a unit of precision
that should be used.
a) How old are you?
b) How much does a feather weigh?
c) How much gas did you put in your car?
d) How thick is this piece of paper?
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Grade 12 Essentials – Precision Measurement
2. Andre is measuring the voltage put out by a 9 volt battery. He measures
the output to be 2.6843 volts.
a) Is his measurement precise? Why or why not?
b) Is his measurement accurate? Why or why
not?
3. Louise buys a chocolate bar that states its weight is 88g. After measuring
the weight, she finds it to be 87 g.
a) Is her measurement precise? Why or why not?
b) Is her measurement accurate? Why or why not?
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Grade 12 Essentials – Precision Measurement
NOTE: Questions 4 and 5 are likely to be on your test and final exam. There are
many justification questions in this unit!
4. Describe an example of a measurement that is precise but not accurate.
5. Describe an example of a measurement that is accurate but not precise.
6. A doctor measures a newborn baby in centimeters and finds the
measurement to be 53.47 cm. The mother uses a tape measure and finds
the measurement to be 52 cm.
a) What is the precision of the doctor’s measurement device?
b) What is the precision of the mother’s measurement device?
c) How accurate is the mother’s measurement?
7. Gold is trading at $1 300 per ounce. Explain why a jeweller would want to
be very accurate when weighing gold to make a ring.
6
Grade 12 Essentials – Precision Measurement
8. The label on a large package of Gushers state that the bag
contains 240 pieces. Ten bags are selected at random and the number of
pieces in each bag is counted. The bags are found to contain the
following number of Gushers:
a) What is the mean number of Gushers per bag?
b) What is the trimmed mean if the top and bottom scores are removed?
c) What is the weighted mean of each score below 240 is weighted as 3,
each score above 240 is weighted at 2, and scores of exactly 240 are
weighted as 1?
d) What is the precision of these samples?
e) What is the accuracy when the mean in a) is compared to the accepted
value?
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Grade 12 Essentials – Precision Measurement
Uncertainty: Notes
Results of measurement depend on:
- the precision of the _________________________
- the skill of the ___________________ reading the results
Uncertainty is the
of a measurement
If not stated, use half of the precision of the measuring device
We often refer to this in everyday life as “give or take”
A measured value can take into account uncertainty:
measured value ± measurement uncertainty
NOTE: When adding or subtracting measurements that each have an
uncertainty, the combined value will also have an uncertainty. The uncertainty
of the final amount is the
of the measured uncertainties.
Example 1) A gardener mixes fertilizer with 1 L of water. The water jug has lines
showing the volume every 0.1 L. What is the actual volume of water, including
uncertainty?
Example 2) A ruler measures in cm to one decimal place. Using this ruler, a
pencil is measured as accurately as possible and it is found to be 7.8 cm long.
a) What is the precision of this ruler?
b) What is the uncertainty of any measurement made with this ruler?
c) What is the actual measurement of the pencil with uncertainty?
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Grade 12 Essentials – Precision Measurement
Example 3) A load is made up of three parts. The mass of the first part is 56 kg,
the mass of the second part is 100 kg, and the mass of the third part is 78 kg.
What is the maximum and minimum weight of the load?
a) Find precision.
b) Calculate the uncertainty.
c) Find the combined mass.
d) Find the combined uncertainty.
e) Calculate the minimum and maximum weight.
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Grade 12 Essentials – Precision Measurement
Uncertainty: Practice
1. Circle the measurement that is more precise.
a)
b)
c)
d)
e)
10.8 m
4.6 g
5
2 6 hours
or
or
or
8.75 miles or
7
8 16 inches or
15 m
14.23 kg
11 hours 40 minutes
6.75 yards
5
3 32 inches
2. For each of the following measurements, state the precision of the
instrument and the measurement including uncertainty.
Measurement
Precision
Measurement (complete with uncertainty)
5 cm
16.3 kg
7.54 km
15 minutes
12 years old
6 ¾ inches
3. A plumber calculates that he needs 2.05 m of pipe. State the
measurement with uncertainty.
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Grade 12 Essentials – Precision Measurement
4. Fred measures the radius of a circle and finds the radius to be 35.75 mm.
a) State the precision of the measuring device.
b) State the uncertainty of the measuring device.
c) State the measurement Fred should report including uncertainty.
d) What is the maximum and minimum value of the actual measurement?
5. Examine the following measurement:
a) What is the precision of the measuring device?
b) What is the length of the measured item, including its uncertainty?
6. A manufacturer drills a hole in a board. An employee measures the
diameter of the hole to be 4.37 mm. She knows that the device used to
measure the hole has an uncertainty of 0.02 mm. Express the minimum
and maximum diameters of the hole in mm.
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Grade 12 Essentials – Precision Measurement
7. Leo works at the post office and calculates the total shipping weight of
two packages being sent to Sachs Harbour, NT. The packages weigh
214.3 kg and 5.0 kg.
a) What are the uncertainties of the package weights?
b) What is the combined weight with uncertainty?
c) What is the combined min and max if the packages are shipped
together?
8. A kitchen cabinet maker is installing two cabinets side by side. Each
cabinet is 76.3 cm wide. What is the max and min of their combined
width? [NOTE: See example 3 from your notes]
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Grade 12 Essentials – Precision Measurement
Tolerance: Notes
In manufacturing, no two objects are exactly the same. There is an allowance
for error up to a certain limit so that parts will still fit properly.
Tolerance level is the range of
production of an object. It is set by designers or engineers.
Nominal value is the
value is usually
in the
for a measurement. The target
between the minimum and maximum values.
Tolerance = maximum limit – minimum limit
Four methods of stating tolerance levels:
maximum value
minimum value
minimum value
+ tolerance
-0
1
nominal value ± 2(tolerance)
maximum value + 0
- tolerance
Example 1) A measurement calls for 2.9947 ± 0.0004 cm.
a) What is the measurement’s upper and lower limits?
b) What is the tolerance?
c) What is the nominal value?
d) What is the tolerance level?
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Grade 12 Essentials – Precision Measurement
Example 2) State the tolerance level the other three ways given the
measurement for a drilled hole in a tractor part is 8.231 ± 0.002 cm.
Example 3) Mackenzie is making caramel candies. The recipes says to use a
thermometer to monitor the temperature of the sugar mixture. If it is not heated
enough candies will not hold their shape. If it is heated too much the candies
will be too firm. The sugar mixture must be heated between 245º F and 250º F.
a) What is the temperature tolerance of the mixture?
b) Write the acceptable temperature range in each of the four ways shown.
DISCUSS: What are some real world applications of tolerance?
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Grade 12 Essentials – Precision Measurement
Tolerance: Practice
1. Use the following maximum and minimum measurement values to state
tolerance levels (state the tolerance level in all four ways).
a) maximum = 25.75 mm
minimum = 25.25 mm
b) maximum = 22ºC
minimum = 16 ºC
2. Adam is a tailor. He is sewing a pair of pants for a client. The waist
measurement must be between 33.75 in and 34.25 in.
a) What are the nominal value and the ± range of the waist
measurement?
b) What is the tolerance?
+ tolerance
c) Write the dimension in the form minimum value - 0
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Grade 12 Essentials – Precision Measurement
3. A part being manufactured in a machine shop has a maximum allowable
dimension of 16.28 mm and a minimum of 16.16 mm.
a) What is the manufacturing tolerance?
1
b) Write the dimension in the form nominal value ± 2(tolerance)
c) Write the dimension in the form maximum value
minimum value
4. An engineering drawing states that a certain part has the following
4.22
length:
4.00
mm
Express the nominal value and tolerance for this part in mm.
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Grade 12 Essentials – Precision Measurement
5. Write the maximum and minimum values represented by each of the
following dimensions.
a)
b)
c)
d)
6. NOTE: THIS WILL MOST LIKELY BY A QUESTION ON YOUR EXAM (or something
very similar):
Tolerance is often used in construction, commercial, industrial, or artistic
applications.
a) State a specific example where tolerance is used.
b) Support your example with a written explanation of how tolerance
is used.
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Grade 12 Essentials – Precision Measurement
Chapter Review
Definitions: You will be expected to know the following
definitions for this unit. You do not need to memorize a
specific definition. Just make sure that you have a basic
understanding of the following terms …
 Accuracy
 Precision
 Uncertainty
 Tolerance
 Nominal Value
Short Answer/Problem Solving:
1. Explain if the following measurements would give an accurate measure
and if the measuring decide is appropriate. State why or why not.
a) Using the length of your forearm to measure the length of a picnic
table.
b) Using a metre stick to calculate the distance between two cities.
2. Christ owns a candy factory that specializes in making chocolate candies.
Explain why Christ needs to be very accurate when measuring his
ingredients.
3. Would it be possible to accurately tell the time on a watch
face that has no numbers? Why or why not?
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Grade 12 Essentials – Precision Measurement
4. For each of the following measurements, state the precision of the
instrument and the measurement including uncertainty.
Measurement
Precision
Measurement (complete with uncertainty)
45 min
36.8ºC
1.24379 g
45.5 m
3.5 hours
6
7
16
inches
5. Geneviève is mixing juice in a jug marked in quarter-litres. She measures
the amount of juice in the jug to be 2.5 L.
a) Write the measurement of juice in the jug with the uncertainty.
b) What is the range of volume (in litres) that could be in the jug?
6. Marcia’s oven indicates temperatures to the nearest 10ºC. She sets it at
160ºC.
a) What are the precision and uncertainty of the oven thermometer?
b) What is the maximum possible temperature in the oven? What is the
minimum possible temperature?
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Grade 12 Essentials – Precision Measurement
7. A graduated cylinder is a measuring device used for
liquids. Express the precision and uncertainty for the
given graduated cylinder.
8. A kitchen installer is laying out a kitchen design. She measures the fridge
to be 71 ± 0.5 cm and the stove to be 76 ± 0.5 cm. What is the combined
width?
9. A shipping clerk calculates the total shipping weight of 3 packages with
individual weights of 16.5 kg, 2.8 kg and 1.4 kg. What is the total weight of
the package and its uncertainty?
10. In the following expression, what are the nominal, minimum and maximum
values?
25 lbs ± 0.5 lbs
Nominal:
Maximum:
Minimum:
11. Express the tolerance of the following using the minimum and maximum
values.
20
a) 1.45 ± 0.02 g
Maximum:
Minimum:
b) 27 ± 0.5 mL
Maximum:
Minimum:
Grade 12 Essentials – Precision Measurement
12. Write the following maximum and minimum values in the form
1
nominal value ± 2(tolerance).
a) maximum = 25.75 mm; minimum = 25.25 mm
b) maximum = 16ºC; minimum = 22ºC
c) maximum = 20”; minimum = 19”
13. An electrical resistor has resistance with a nominal value of 100 ohms and
a tolerance of 3%.
a) What is the range of acceptable values, in ohms, for the resistor?
1
b) Write the resistance in the form nominal value ± 2(tolerance).
NOTE: One of the following questions will be asked on the test.
14. Tolerance is often used in construction, commercial, industrial, or artistic
applications.
 State a specific example where tolerance is used.
 Support your example with a written explanation, or with other
information or evidence, of how tolerance is used.
15. State a measurement situation where a degree of precision would be
required. Justify your answer.
16. Describe a measurement situation and explain why a certain degree of
accuracy would be required.
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