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Learning objectives
 Use the
SI system.
 Know the SI base units.
 State rough equivalents for the SI base units in the English system.
 Read and write the symbols for SI units.
 Recognize unit prefixes and their abbreviations.
 Build derived units from the basic units for mass, length, temperature, and time.
 Convert measurements from SI units to English, and from one prefixed unit to another.
 Use derived units like density and speed as conversion factors.
 Use percentages, parts per thousand, and parts per million as conversion factors.
 Use and report measurements carefully.
 Consider the reliability of a measurement in decisions based on measurements.
 Clearly distinguish between
 Count the number of significant figures in a recorded measurement.
Record measurements to the correct number of digits.
 Estimate the number of significant digits in a calculated result.
 Estimate the precision of a measurement by computing a standard deviation.
Lecture outlineMeasurement is the collection of quantitative data. The proper handling and
interpretation
of measurements are essential in chemistry  and in any scientific endeavour.
To use measurements correctly, you must recognize that measurements are not
numbers. They always contain a unit and some inherent error.
The second lecture focuses on an international system of units (the SI system)
and introduces unit conversion. In the third lecture, we'll discuss ways to recognize, estimate and report the errors that are always present in measurements.
Measurement
 quantitative observations
 include 3 pieces of information
 magnitude
 unit
 uncertainty
 measurements are not numbers
 numbers are obtained by counting or by definition; measurements are obtained by comparing an object with a standard "unit"
 numbers are exact; measurements are inexact
 mathematics is based on numbers; science is based on measurement

The National Institute of Standards and Technology (NIST) has published several online guides for users of the SI system.  
The SI System
 Le Systéme Internationale (SI) is a set of units and notations that are standard in science.
Four important SI base units
(there are others)
Quantity 
SI Base Unit 
English Equivalent 
length 
meter (m) 
1 m = 39.36 in 
mass 
kilogram (kg) 
1 kg = 2.2 lbs 
time 
second (s) 

temperature 
kelvin (K) 
°F = 1.8(^{o}C)+32
K = °C + 273.15


 derived units are built from base units
Some SI derived units
Quantity 
Dimensions 
SI units 
Common name 
area 
length × length 
m^{2} 
square meter 
velocity 
length/time 
m/s 
density 
mass/volume 
kg/m^{3} 
frequency 
cycles/time 
s^{1} 
hertz (Hz) 
acceleration 
velocity/time 
m/s^{2} 

force 
mass × acceleration 
kg m/s^{2} 
Newton (N) 
work, energy, heat 
force × distance 
kg m^{2}/s^{2} 
Joule (J) 


Prefixes are used to adjust the size of base units
Commonly used SI prefixes (there are others).
Prefix 
Meaning 
Abbreviation 
Exponential
Notation 
Giga 
billion 
G 
10^{9} 
Mega 
million 
M 
10^{6} 
kilo 
thousand 
k 
10^{3} 
centi 
hundredths of 
c 
10^{2} 
milli 
thousandths of 
m 
10^{3} 
micro 
millionths of 
µ 
10^{6} 
nano 
billionths of 
n 
10^{9} 
pico 
trillionths of 
p 
10^{12} 

 several nonSI units are encountered in chemistry
Non SI unit 
Unit type 
SI conversion 
Notes 
liter (L) 
volume 
1 L = 1000 cm^{3} 
1 quart = 0.946 L 
Angstrom (Å) 
length 
1 Å = 10^{10} m 
typical radius of an atom 
atomic mass unit (u) 
mass 
1 u = 1.66054×10^{27} kg 
about the mass of a proton or neutron; also known as a 'dalton' or 'amu' 


 
Arithmetic with units
 addition and subtraction: units don't change
2 kg + 3 kg = 5 kg
412 m  12 m = 400 m
 consequence: units must be the same before adding or subtracting!
3.001 kg + 112 g = 3.001 kg + 0.112 kg = 3.113 kg
4.314 Gm  2 Mm = 4.314 Gm  0.002 Gm = 4.312 Gm
 multiplication and division: units multiply & divide too
3 m × 3 m = 9 m^{2}
10 kg × 9.8 m/s^{2} = 98 kg m/s^{2}
 consequence: units may cancel
5 g / 10 g = 0.5 (no units!)
10.00 m/s × 39.37 in/m = 393.7 in/s

 
Converting Units
 5 step plan for converting units
 identify the unknown, including units
 choose a starting point
 list the connecting conversion factors
 multiply starting measurement by conversion factors
 check the result: does the answer make sense?
 Common variations
 series of conversions
 example:
Americium (Am) is extremely toxic; 0.02 micrograms is the allowable body burden in bone. How many ounces of Am is this?
 converting powers of units
 converting compound units
 starting point must be constructed
 using derived units as conversion factors
 mass fractions (percent, ppt, ppm) convert mass of sample into mass of component
 density converts mass of a substance to volume
 velocity converts distance traveled to time required
 concentration converts volume of solution to mass of solute
Uncertainty in Measurements
 making a measurement usually involves comparison with a unit or a scale of units
 always read between the lines!
 the digit read between the lines is always uncertain
 convention: read to 1/10 of the distance between the smallest scale divisions
 significant digits
 definition: all digits up to and including the first uncertain digit.
 the more significant digits, the more reproducible the measurement is.

counts and defined numbers are exact they have no uncertain digits!

Tutorial: Uncertainty in Measurement  
 counting significant digits in a series of measurements
 compute the average
 identify the first uncertain digit
 round the average so the last digit is the first uncertain digit

counting significant digits in a single measurement
 convert to exponential notation
 disappearing zeros just hold the decimal point they aren't significant.
 exception: zeros at the end of a whole number
might be significant
 Precision of Calculated Results
 calculated results are never more reliable than the measurements they are built from
 multistep calculations: never round intermediate results!
 sums and differences: round result to the same number of
fraction digits as the poorest measurement
 products and quotients: round result to the same number of
significant digits as the poorest measurement.

Quiz Using Significant Figures  
 Precision vs. Accuracy
good precision & good accuracy poor accuracy but good precision 

good accuracy but poor precision poor precision & poor accuracy 
Precision 
Accuracy 
reproducibility 
correctness 
check by repeating measurements 
check by using a different method 
poor precision results from poor technique 
poor accuracy results from procedural or equipment flaws 
poor precision is associated with 'random errors'  error has random sign and varying magnitude. Small errors more likely than large errors. 
poor accuracy is associated with 'systematic errors'  error has a reproducible sign and magnitude. 
 Estimating Precision
 Consider these two methods for computing scores in archery competitions. Which is fairer?
 Score by distance from bullseye 
 Score by area or target 
 The standard deviation, s, is a precision estimate based on the area score:
where
x_{i} is the ith measurement
is the average measurement
N is the number of measurements.

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General Chemistry Online! MeasurementCopyright © 19972005 by Fred Senese Comments & questions to fsenese@frostburg.edu Last Revised 06/16/05.URL: http://antoine.frostburg.edu/chem/senese/101/measurement/index.shtml
