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Measurement
Measurement – a quantity that has both a
number and a unit.
• Measurements are fundamental to the experimental
sciences
• Units typically used in the sciences are the
International System of Measurements (SI)
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Scientific Notation
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Scientific Notation:
A method of representing very large or
very small numbers in the form:
M x 10n
 M is a number between 1 and 10
 n is an integer
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
Review:
Scientific notation expresses a
number in the form:
M x
1  M  10
n
10
n is an
integer
Nature of Measurement
Measurement - quantitative observation
consisting of 2 parts
•
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63 x 10-34 Joule seconds
Uncertainty in Measurement
A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
Precision and Accuracy
Accuracy – measure of how close a measurement
comes to the actual or true value of whatever is
being measured.
Precision – measure of how close a series of
measurements are to one another.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Why Is there Uncertainty?
 Measurements are performed with instruments
 No instrument can read to an infinite number of
decimal places
Which of these balances has the greatest
uncertainty in measurement?
Determining Error
Accepted Value – the correct
value based on reliable references
Experimental Value – the value
measured in the lab
Error(can be +or-)=experimental value – accepted value
Percent error = absolute value of error x 100%
accepted value
Significant Figures in
Measurement
In a supermarket, you can use the scales to
measure the weight of produce.
If you use a scale that is calibrated in 0.1 lb
intervals, you can easily read the scale to the
nearest tenth of a pound.
You can also estimate the weight to the nearest
hundredth of a pound by noting the position of the
pointer between calibration marks.
Significant Figures in
Measurement
If you estimate a weight that lies between 2.4 lbs
and 2.5 lbs to be 2.46 lbs, the number in this
estimated measurement has three digits.
The first two digits (2 and 4 ) are known with
certainty.
The rightmost digit (6) has been estimated and
involves some uncertainty.
Significant Figures in
Measurement
Significant figures in a measurement include all of
the digits that are know, plus a last digit that is
estimated.
Measurements must always be reported to the
correct number of significant figures because
calculated answers often depend on the number
of significant figures in the values used in the
calculation.
Rules for Counting Significant
Figures
Nonzero integers always count as
significant figures.
3456 m has
4 sig figs.
Rules for Counting Significant
Figures
Leading zeros NEVER count as
significant figures.
0.0486 cm has
3 sig figs.
Rules for Counting Significant
Figures
Captive zeros (ones that are being
hugged by sig figs) always count as
significant figures.
16.07 mm has
4 sig figs.
Rules for Counting Significant
Figures
Zeros at the end of a number are
significant only if you can see the
decimal point.
9.000 m has
4 sig figs
1050.0 mm has
5 sig figs
Rules for Counting Significant
Figures
Zeros at the end are not
significant if you can’t see the
decimal point.
7000 m has
1 sig fig
27210 m has
4 sig figs
Rules for Counting Significant
Figures
Exact numbers have an infinite
number of significant figures.
1 meter = 100 cm
Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
0.0054 cm 
2 sig figs
3,200,000 m 2 sig figs
Questions
1) 78ºC, 76ºC, 75ºC 2) 77ºC, 78ºC, 78ºC
3) 80ºC, 81ºC, 82ºC
The sets of measurements were made of the boiling
point of a liquid under similar conditions. Which
set is the most precise?
Set 2 – the three measurements are closest together.
What would have to be known to determine which set
is the most accurate?
The accepted value of the liquid’s boiling point
Questions
How do measurements relate to experimental
science?
Making correct measurements is fundamental to the
experimental sciences.
How are accuracy and precision evaluated?
Accuracy is the measured value compared to the
correct values. Precision is comparing more than
one measurement.
Questions
Why must a given measurement always be reported to the
correct number of significant figures?
The significant figures in a calculated answer often depend on
the number of significant figures of the measurements
used in the calculation.
How does the precision of a calculated answer compare to the
precision of the measurements used to obtain it?
A calculated answer cannot be more precise than the least
precise measurement used in the calculation.
Question
Determine the number of significant figures in each of
the following
11 soccer players
unlimited
0.070 020 meter
5
10,800 meters
3
5.00 cubic meters
3