Chapter 2.
Measurement
Chemistry is a physical science, one
that depends heavily on measurement
to obtain quantitative data.
Measurement is the determination of
dimensions, capacity, quantity, or
extent of something.
Precision, Accuracy, Error
Precision, Accuracy, Error
Precision refers to the reproducibility of a
given measurement.
Accuracy refers to the agreement between a
measurement (or average several measurements) to the true or accepted value.
Errors are deviations (differences) between
the true value and a measurement. They
can be random or systematic.
Uncertainty in Measurement
All measurements contain some error, or
uncertainty.
Heisenberg's Uncertainty Principle is a natural
law that states that the act of observing
something changes it. In its mathematical
form, it states the limits of accuracy in a
measurement.
Uncertainty in Measurement
Generally, uncertainty is minimized (accuracy
is maximized) by using equipment that is
better designed, more expensive, and more
demanding to use.
Beaker  1 milliliter
$3.00
Cylinder  0.1 milliliter $6.00
Buret
 0.01 milliliter $90.00
Uncertainty in Measurement
Uncertainty in Measurement
Numbers express uncertainty.
Exact numbers contain no uncertainty. They
are obtained by counting objects (integers) or
are defined, as in some conversion factors.
Inexact numbers contain uncertainty. They
are obtained from measurements. The uncertainty in a measurement is shown by the
number of digits recorded.
Uncertainty in Measurement
Significant figures are the digits in a measurement that are known with certainty, plus one
digit that is uncertain. Last digit is uncertain.
14.3 gallons
 0.1 gal
(13 oz)
14.325 gallons  0.001 gal (¾ tsp)
Uncertainty in Measurement
Significant figures allow us to estimate the
uncertainty of a value:
10 +/– 1
1 x 100% = 10%
10
10.0 +/– 0.1
0.1 x 100% = 1%
10.0
10.00 +/– 0.01
0.01 x 100% = 0.1%
10.00
Uncertainty in Measurement
Significant figures and measurements:
With digital instruments (reading is numbers)
record all digits from the instrument. The last
digit is uncertain and may fluctuate.
With analog instruments (reading is a scale)
"read between the lines" for last digit. That
digit is an estimate, and contains uncertainty.
Working with "Sig Figs"
How many significant figures are there
in each of these numbers?
14.3 gallons
14.325 gallons
14.0 gallons
0.025 gallons
Working with "Sig Figs"
In a number from a measurement:
All nonzero digits are significant.
Internal zeroes are significant.
Leading zeroes are not significant.
Trailing zeroes are significant if there
is a decimal point in the number.
Working with "Sig Figs"
How many significant figures
in each number?
1800
1800.
1800.00
Working with "Sig Figs"
Why does this matter? Because we usually
do calculations on measurements.
I ride my bike to school. The distance is 4.1
miles. The other day it took 25.7 minutes.
What was my average speed, in miles per
minute, and in miles per hour?
4.1 mi = 0.1595440793 mi
25.7 min
min
4.1 mi = 0.16 mi = 9.6 mi
25.7 min
min
hr
Working with "Sig Figs"
Why did I convert 0.1595440793 mi/min to
0.16 mi/min and not something else?
Rules for working with significant figures:
Rounding
Sig figs in calculations
Working with "Sig Figs"
Rounding numbers is disposing of nonsignificant digits
Only do this in calculations!
Do not round off measurements!
Working with "Sig Figs"
Rules for rounding:
1. Decide how many digits are significant.
2. Underline them (till you catch on)
3. Look at digit to right of last underlined digit
a. If it's 1  4, drop it.
b. If it's 5  9, add 1 to last sig. fig.
Working with "Sig Figs"
Examples:
Round the following values to 3 sig. figs.
27.428
39.572
0.01565
Calculating with "Sig Figs"
Rules for Calculations:
1. Multiplication and division:
The result has the same number of sig figs
as the value with the fewest sig figs.
4.1 mi = 0.1595440793 mi
25.7 min
min
4.1 mi = 0.16 mi = 9.6 mi
25.7 min
min
hr
Calculating with "Sig Figs"
Rules for Calculations:
2. Addition and Subtraction:
The result has the same uncertainty as the
value with the greatest uncertainty.
Keep digits as far to the right as all values
have sig figs.
23.456
+ 82.9
106.356 ~ 106.4
100.423
-100.312
0.111
Calculating with "Sig Figs"
Examples:
Calculate the quantities, and round to the
correct number of significant figures:
15.86 x 2.34  12.356 =
907.369 – 15.5 =
(143.289 – 139.143) =
187.467
Calculating with "Sig Figs"
Rules for Calculations:
4. Working with exact and inexact numbers:
Exact numbers don't have sig figs because
they don’t introduce uncertainty.
Just use sig figs in inexact numbers
0.16 mi x 60 min = 9.6 mi
min
hr
hr
60 min/hour is an exact conversion
Calculating with "Sig Figs"
Rules for Calculations:
5. If your calculator gives you fewer sig figs
than the value should have, add zeroes
0.465 x 0.200 = 0.0930
4.389 – 2.589 = 1.800
Calculating with "Sig Figs"
Rules for Calculations:
6. If your calculator gives you more digits to
the left of the decimal than are significant,
use scientific notation.
75.3 x 24.8 x 675 = 1260522
= 1.26 x 106
Scientific Notation
Scientific notation is a numerical system in
which a decimal number is expressed as
the product of a number between 1 and 10,
and 10 raised to a power.
1260522 = 1.260522 x 1,000,000
= 1.260522 x 106
= 1.26 x 106
1.26 is the coefficient
106 is the exponential term
Scientific Notation
Scientific notation is useful for expressing
very large or very small numbers.
93,000,000 miles from earth to sun
9.3 x 107 miles
0.000 000 000 000 000 000 000 030 grams
3.0 x 10-23 grams is mass of 1 water molecule
Scientific Notation
When should scientific notation be used?
1. It MUST be used if you have more digits
than significant digits to the left of the
decimal point.
2. It CAN be used whenever it's convenient.
Often, this involves very small numbers.
Summary
It’s easy to keep track of significant figures
if you remember WHY you’re doing it.
WHY are you doing it?
Significant figures reflect the accuracy of
measured quantities and of results
calculated from measured quantities.