Name: ______________________ Group members: ______________________________________________
SPH3U Accuracy, Measurement, Significant Digits
Making careful measurements is at the heart of much scientific activity. Galileo was one of the first
scientists to make careful measurements to prove theories (e.g. he studied balls rolling down an incline
to study the behaviour of falling objects).
What might be some situations in everyday life where accurate measurement would be important?
Accuracy and Precision
What is accuracy? What is precision? We often
use these terms interchangeably in everyday life,
but this is not correct in science. Consider the
following definitions:
High accuracy, high
precision
High precision, low
accuracy
High accuracy, low
precision
Low accuracy, low
precision
Accuracy: how close a measurement is to the actual,
accepted (true) value.
Precision: how close a measurement is to other
measurements.
Using these definitions, draw sets of 3 arrows
(representing measurements) on the targets to the
right to illustrate the described situation.
What does the centre of the target represent?
Activity: Measurement
In your groups, get a ruler and a stop watch. Measure the following as accurately as possible:
Quantity to be Measured
The number of people in the room
The distance from the back window to
the front blackboard
The thickness of one of your hairs
The number of tiles that make up the
floor
The time taken for a pencil to drop from
the height of the desk to the floor
(perform this 6 times and record your
data in the space to the right)
Your Measurement(s)
Challenges in making
accurate measurements
Discussion
1. For a given quantity, we may obtain a range of measurements. What do we do in this case and why?
2. For the pencil drop activity, our repeated measurements produced a range of values; i.e. our
measurements have uncertainty in them. What factors might account for the uncertainty of your
measurements in this activity? Which of these factors probably affect the accuracy of your
measurement the most?
3. What might we do to reduce the uncertainty in our pencil drop measurements? Why can we not
completely eliminate all uncertainty in our measurements?
In your groups, read and discuss:
Uncertainty and Significant Digits (Sig. Digs.)
In the past, you may have learned some rules regarding
significant digits (sig. digs.). The purpose of these rules
was to help you express the amount of uncertainty in a
calculation involving measured values.
Example 1: a measurement of 12.3 m (3 sig. digs.)
indicates that the 12 m is certain but that there is
uncertainty in the “.3” (the actual value might be 12.2 m
or 12.5 m). How many significant digits does 2598
nanoseconds have, and what does it mean?
Example 2: What is the difference between stating a
measurement is 12.3 m (3 sig. digs.) and stating it as
12.30 m (4 sig. digs.)?
In real life, we usually report a calculated result based
on measurements as 2 numbers: the best or average
number (m), and the uncertainty (σ – Greek letter
sigma), written as m ± σ. This is interpreted as saying
that “m is our best estimation, but the true value could
be as high as m + σ, or as low as m – σ.”
Example 3: If the average height of the class is reported
as 165 ± 12 cm, how tall (or short) are the tallest and
shortest members of the class likely to be?
This year, we will simplify how we report results or
textbook calculations. (We will do more with
uncertainty in grade 12 physics):
 When recording results, just use 3 sig. digs. in
scientific notation to avoid rounding error. e.g. your
calculator reads: 23 162, you write 2.32 × 104
 For middle steps in calculations, keep 1 or 2 extra
digits to help reduce rounding error.
 For convenience, we will write 5 instead of 5.00 with
the understanding that it has 3 sig. digs.