Measurement
In this course we will be measuring using the “metric system” Really
called the SI system. We need to be both accurate and precise in our
measurements.
Precision is the degree of being able to produce the same results over and
over again. Some people like to think of this as being a property of the tool
being used. They might say that one ruler is more precise than another.
Accuracy is the degree to which a measurement agrees with other
people’s measurement. It is possible to have a precision instrument that is
not accurate (a very good ruler that has the first .3 cm broken off).
We need to extent this reasoning to include SIGNIFICENCE of measurement
(Chapter 3 of your text book)
The two basic rules of doing math with significant figures are:
Rule #1:
KNOW!
When adding and subtracting you must “line up” the decimals and report the digits that you
Rule #2:
When multiplying and dividing your answer can not contain more significant figures than the
lowest number of significant figures used in the calculation.
(Remember that WHOLE numbers are exact and unlimited significance)
The seven basic quantities included in SI system of measurement are:
1. Length
2. Mass
3. Time
4. Current
5. Temperature
6. Amount of substance (mole)
7. Luminous intensity
The corresponding seven basic units with their symbols are defined here
(as officially defined):
1: meter (m): It is the length of the path travelled by light in vacuum during a time interval of
1/299 792 458 of a second.
2: kilogram (kg): It is equal to the mass of the international prototype of the kilogram. The
prototype is a platinum-iridium cylinder kept at International Bureau of Weights and Measures,
at Severes, near Paris, France.
3: time (t): It is the duration of 9, 192, 631, 770 periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the cesium-133 atom.
4: ampere (A) : It is that constant current which, if maintained in two straight parallel
conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in
vacuum, would produce between these conductors a force equal to 2x10 −7 newton per meter of
length.
5: kelvin (K): It is the fraction 1/273.16 of the thermodynamic temperature of the triple point of
water.
6: mole (mol): It is the amount of substance of a system which contains as many elementary
entities as there are atoms in 0.012 kilogram of carbon 12.
7: candela (cd): It is the luminous intensity, in a given direction, of a source that emits
monochromatic radiation of frequency 540x1012 hertz and that has a radiant intensity in that
direction of 1/683 watt per steradian (measure of solid angle).
MKS system of units vs. CGS system of units (physics or chemistry)
MKS is an abbreviation of Meter, Kilogram and Second. These three quantities form the basic set of units in
MKS system. Clearly, it is a subset of SI system of units. As we can realize, mechanics - a branch of physics involves only length, mass and time. Therefore, MKS system is adequate to represent quantities used in
mechanics.
CGS is an abbreviation of Centimeter, Gram and Second. These are the units most often used in chemistry and
it is imperative that simple conversions like these are made easily.
This distinction between mechanics and rest of physics is hardly made in recent time. We can, therefore,
completely do away with MKS nomenclature in favor of SI system.
Si prefixes below are the 20 currently accepted System International (SI) prefixes and their meanings
A list of the 7 base units is on page 33 of the Chemistry text on page 33 is a partial list of the prefixes
prefix symbol value
yotta
Y
1024
zetta
Z
1021
exa
E
1018
peta
tera
giga
mega
kilo
hecto
deca
P
T
G
M
k
h
da
1015
1012
109
106
103
102
101
100
deci
centi
milli
micro
nano
d
c
m
u
n
10-1
10-2
10-3
10-6
10-9
pico
p
10-12
femto
f
10-15
atto
a
10-18
zepto
z
10-21
yocto
y
10-24
expanded value
English name
U.S. septillion; U.K.
1 000 000 000 000 000 000 000 000
quadrillion
1 000 000 000 000 000 000 000 U.S. sextillion
U.S. quintillion; U.K.
1 000 000 000 000 000 000
trillion
1 000 000 000 000 000 U.S. quadrillion
1 000 000 000 000 U.S. trillion; U.K. billion
1 000 000 000 U.S. billion
1 000 000 million
1 000 thousand
100 hundred
10 Ten (Not usually used)
Base unit of meter, gram, watt, liter,
one
etc.1
0.1
tenth
0.01
hundredth
0.001
thousandth
0.000 001
millionth
0.000 000 001
U.S. billionth
U.S. trillionth; U.K.
0.000 000 000 001
billionth
0.000 000 000 000 001
U.S. quadrillionth
U.S. quintillionth; U.K.
0.000 000 000 000 000 001
trillionth
0.000 000 000 000 000 000 001
U.S. sextillionth
U.S. septillionth; U.K.
0.000 000 000 000 000 000 000 001
quadrillionth
Highlighted information is more commonly used; know these!!! (also listed on page 33 of
text)
Temperature and Pressure conversions
In your everyday life and in your study of Chemistry, you are likely to encounter three different temperature scales and several units for
measuring pressure. When you watch the weather report on the news, they will report the temperature on one scale, yet you measure temperature
in the laboratory on a different scale. Many Chemistry equations must be done using yet another temperature scale. Clearly, you can see the
importance of the use of units when reporting temperature and pressure. You can also see the need, for a student of Science, to be able to convert
temperatures from one scale to another and one pressure to another.. This page is designed to help you do just that.
The Fahrenheit Scale - The Fahrenheit scale is the scale that is used when they report the weather on the news each night. It is probably the
temperature scale that you are most familiar with, if you live in the United States.
The Celsius Scale - The Celsius scale is commonly used for scientific work and most countries of the world. The thermometers that we use in
our laboratory are marked with the Celsius scale. The Celsius scale is also called the Centigrade scale because it was designed in such a way that
there are 100 units or degrees between the freezing point and boiling point of water. One of the limitations of the Celsius scale is that negative
temperatures are very common. Since we know that temperature is a measure of the kinetic energy of molecules, this would almost suggest that
it is possible to have less than zero energy. This is why the Kelvin scale was necessary.
The Kelvin Scale - The International System of Measurements (SI) uses the Kelvin scale for measuring temperature. This scale makes more
sense in light of the way that temperature is defined. The Kelvin scale is based on the concept of absolute zero, the theoretical temperature at
which molecules would have zero kinetic energy. Absolute zero, which is about -273.15 oC, is set at zero on the Kelvin scale. This means that
there is no temperature lower than zero Kelvin, so there are no negative numbers on the Kelvin scale. For certain calculations, like the gas laws,
which you will be learning soon, the Kelvin scale must be used.
Comparison of Temperature Scales at Normal Pressure
Comparison Points
Fahrenheit
Celsius
Kelvin
water boils
212
100
373
body temperature
98.6
37
310
water freezes
32
0
273
absolute zero
-460
-273
0
There will be times when you need to be able to convert a temperature from one scale to another. In real life, you might be in a country where
temperature is reported in Celsius and you will want to convert that into Fahrenheit, in order to figure out if you need to wear a sweater. In your
laboratory work, you may need to change from Celsius to Kelvin in order to calculate the volume that a gas might occupy at standard temperature
and pressure. The table below will show you the formulas that you can use to change from one scale to another.
Temperature Conversion Formulas
Conversion
Celsius to Kelvin
Formula
K = C + 273
Example
21oC = 294 K
Kelvin to Celsius
C = K - 273
313 K = 40 oC
Fahrenheit to Celsius
C = (F - 32) x 5/9
89 oF = 31.7 oC
Celsius to Fahrenheit
F = (C x 9/5) + 32
50 oC = 122 oF
* Note, to change back and forth between Fahrenheit and Kelvin is a two step process. Practice these conversions.
0oF = ____________ oC
-150 oC = ____________oF
50 oC = ___________ K
300 K = ____________ oC
-40 oC = ____________oF
-10 oC = ____________oF
105 K = ____________ oC
212oF = ____________
25 oC = ____________oF
68oF = ____________ oC
Is 37oC a good day to go swimming or a good day to go snow skiing?
Pressure is defined as force divided by area.
Pressure = Force / Area
Pressure Affects the Boiling point of liquids. If there is less pressure above a liquid it is
easier for a molecule to escape the liquid as a gas.
LOWERING THE ATMOSPHERIC PRESSURE LOWERS THE BOILING POINT.
As a liquid warms more and more of the liquid evaporates and its vapor pressure increases.
The standard unit of pressure is the Pascal. One Pascal is the pressure exerted by one
Newton of force acting on one square meter of area (it is a very small unit of pressure and
often units of Kilopascals are reported (kPa).
The average atmospheric pressure is “1 atm” but it can be described in several other units.
1 atm = 101.3 kPa = 760 mm Hg = 760 torr
1 atm = about 32 ft H2O = 29.9 in. Hg= 14.7 p.s.i. or lbs/in2
The news caster in the twin cities have become lazy and often say the barometric pressure
is 29.5 and falling (they leave off the 29.5 “inches of mercury” and falling).
Convert the following units of pressure:
5 atm
= __________ mmHg
560 mm Hg
= _________ atm
30.3 in. Hg
= __________ atm
250 kPa
= __________ mm Hg
26.5 in. Hg
= ___________ kPa
Simple metric conversions
Name: _______________________
period: ______
The SI (or System International) units of measurement are often referred to as the metric system in the United States. The SI
is the preferred method of measurement in the scientific community for a variety of reasons. You must be able to convert
units of measure quickly and accurately to be a competent science student.
Remember:
The prefix
Milli means 1/1000
Centi means 1/100
The basic unit are GRAM, METER, and in America LITER
Kilo mean 1,000
There are many other prefixes you should know but the three listed above are by far the most common.
In other parts of the world the unit dm3 (or cubic decimeter) is used rather than liter.
1.
25 mm = _________ meters
11.
25 cm = __________ km *
2.
2 liters = ________ ml
12.
17.3 g = __________mg
3.
500 meters = _________ km
13.
29.3 mg = _______ cg *
4.
10 km = __________meters
14.
500 km = __________ cm *
5.
140 cm = ________ m
15.
2.73 liters = ________ ml
6.
35 m = __________ cm
16.
25.5 mg = __________ grams
7.
200 mg = __________g
17.
25 cm = __________ km *
8.
2.5 grams = __________ mg
18.
50.5 grams = __________ cg
9.
2.5 g = __________ cg
19.
100 km = _______________ mm *
10.
750 ml = __________ l
20.
50.5 gm = __________ kg

indicates the problem may be a 2 step conversion
Convert 53 000 000 to scientific notation
___________________________
0.000 000 000 25 is _____________________________ in scientific notation.
1 783 002 000 000 is _____________________________ in scientific notation.
134.68 is _____________________________ in scientific notation.
8 675 309 000 000 000 000 000 is _____________________________ in scientific
notation.
6.5001 x 10-10 is the same as _______________________________
1.37505 x 10 13 is the same as _______________________________
Now try a few of these harder ones (probably have to look up a few of the prefixes).
21.
25 micrometers = _____________ meters
22.
1.25 milligrams = ________ kg
23.
500 mega bits = _______________ bits
24.
10.3 picometers = _____________nanometers
25.
140 cg = ________ kg
26.
355.7 mega bits = __________ kilo bits
27.
20.701 micrograms per liter = __________milligrams per liter
28.
2.5 decagrams = _____________ mg
29.
2.5 x10 10 meters = _____________ km
30.
2.5 x10 15 millimeters = _____________ km