Transcript Sig Figs

PowerPoint The First
In which you will find information on:
•the metric (SI) system of measurement
• uncertainty in measurements
•how to count sig figs
Units of Measurement
In every measurement there is a
Number followed by a
 Unit from a measuring device
Numbers without a unit are naked numbers
(NN)!
Some Tools for Measurement
Which tool(s)
would you use to
measure:
A. temperature
B. volume
C. time
D. weight
Standards of Measurement
When we measure, we use a measuring tool
to compare some dimension of an object to a
For example, at one time the
standard.
standard for length was the king’s
foot. What are some problems with
this standard?
What do we use in science?
• The metric system – based on units of 10
• Specifically, we use the SI system which has
specific standards for 7 basic units
SI measurement
• Le Système international d'unités
• The only countries that have not
officially adopted SI are Liberia (in
western Africa) and Myanmar
(a.k.a. Burma, in SE Asia), but
now these are reportedly using
metric regularly
• Metrication is a process that does
not happen all at once, but is
rather a process that happens
over time.
• Among countries with non-metric
usage, the U.S. is the only country
significantly holding out. The U.S.
officially adopted SI in 1866.
Information from U.S. Metric
Association
UNITS OF MEASUREMENT
Use SI units — based on the metric
system
Length
Meter, m
Mass
Kilogram, kg
Volume
Liter, L
Time
Seconds, s
Temperature
Celsius degrees, ˚C
kelvins, K
Didn’t I say there were SEVEN base
units?
Find the new ones!
What’s the most important
measurement to chemists?
• The mole!
• A mole is a measure of the # of particles in a
substance.
• Analogy – 1 dozen eggs: 12 eggs as
1 mole atoms : 6.022 x 1023 atoms
Metric Prefixes
• Used for convenience – wouldn’t want to describe the
mass of a penny in kilograms!
• Kilo- means 1000 of that unit
– 1 kilometer (km) = 1000 meters (m)
• Centi- means 1/100 of that unit
– 1 meter (m) = 100 centimeters (cm)
– 1 dollar = 100 cents
• Milli- means 1/1000 of that unit
– 1 Liter (L) = 1000 milliliters (mL)
Metric Prefixes
Metric Prefixes
Units of Length
• ? kilometer (km) = 500 meters (m)
• 2.5 meter (m) = ? centimeters (cm)
• 1 centimeter (cm) = ? millimeter (mm)
• 1 nanometer (nm) = 1.0 x 10-9 meter
O—H distance =
9.4 x 10-11 m
9.4 x 10-9 cm
0.094 nm
Volume = length x length x length
Chemistry In Action
On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mars’
atmosphere 100 km lower than planned and was destroyed by heat.
1 lb = 1 N
1 lb = 4.45 N
“This is going to be the
cautionary tale that will be
embedded into introduction to
the metric system in elementary
school, high school, and college
science courses till the end of
time.”
Uncertainty in Measurement
• When making measurements, one must
always estimate an extra decimal place (if it is
a non-digital display)
• This extra place is uncertain
How many decimal places can you
read on each of these?
Significant Figures
The numbers reported in a measurement are
limited by the measuring tool
Significant figures in a measurement include
the known digits plus one estimated
(uncertain) digit
Significant Figures and Calculations
• Measurements in the lab must be made
accurately!
• But what does that mean?
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known) = 2
Second digit (known)
cm
2.?? cm
= 0.7
2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.75 cm
or
2.74 cm
or
2.76 cm
Known + Estimated Digits
In 2.76 cm…
• Known digits 2 and 7 are 100% certain
• The third digit 6 is estimated (uncertain)
• In the reported length, all three digits (2.76 cm)
are significant including the estimated one
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
cm
5.?? cm
5.0? cm
5.00 cm
ALWAYS estimate ONE place past the smallest mark!
11.51
What happens when measurements
are used in calculations?
• Measurements are only as good as the
instruments used to make them!
• Imagine calculating the volume of a cube with
three different rulers: 2.4 cm x 2.45 cm x 2.453
cm = 14.42364 cm3
• The answer has way too many digits! None of the
rulers were able to measure all 5 decimal places!
• Instead, we use significant figures to show the
accuracy of a measurement.
Counting Significant Figures
RULE 1. All non-zero digits in a measured number are
significant. Only a zero could indicate that rounding
occurred.
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
3
5
Leading Zeros
RULE 2. Leading zeros in decimal numbers are NOT
significant.
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
0.000262 mL
2
3
____
Sandwiched Zeros
RULE 3. Zeros between nonzero numbers are
significant. (They can not be rounded unless they are
on an end of a number.)
Number of Significant Figures
50.8 mm
3
2001 min
4
0.702 lb
3
0.00405 m
3
____
Trailing Zeros
RULE 4. Trailing zeros in numbers without decimals are
NOT significant. They are only serving as place
holders.
Number of Significant Figures
25,000 in.
2
200. yr
3
48,600 gal
3
25,005,000 g
5
HOMEWORK EXERCISES
• These questions are due the next time our class
meets.
1)
For each of the following pieces of glassware, provide a sample
measurement and discuss the number of significant figures and
uncertainty.
CONTINUED…
HOMEWORK CONT’D
2) Which of the following are exact numbers?
a. The elevation of Breckenridge, CO is 9600 ft.
b. There are 12 eggs in a dozen.
3) How many sig figs are in each of the following?
a. 12
b. 1098
c. 2.001 x 103
d. 0.0000101
4) Round each number to 3 sig figs.
a. 312.54
b. 0.00031254
c. 31, 254, 000