Measurement
There are many ways to measure things and not everyone
uses the same units of measure. That’s one reason why
scientists developed an International System (SI) for
standardizing units of measure. While this system has helped
scientists, many people are still unfamiliar with the S.I. system,
since the U.S. refuses to go along with the rest of the world.
Our goal here is to become familiar with the S.I. system as it is
used in the study of chemistry.
Base Units of the S.I. System
Quantity

The following units are Time
the most basic units of
Length
the S.I. system. All
other units are derived Mass
from these basic units.
Base Unit
second (s)
meter (m)
kilogram
(kg)
Temperature kelvin (K)

Notice that the base
Amount of
unit of mass is the
kilogram, not the gram! Substance
Electric
current
mole (mol)
ampere
(A)
Length




To measure length, we
use the meter
A meter is equal to 3.28
ft.
Scientists often need to
accurately measure
things that are either
very small or very big
The micrometer at right
can measure with an
accuracy to 0.001 mm
The “cubit” was not a very precise
unit, since it was based on forearm
length.
Mass

Mass is defined as the amount
of matter. Although the
kilogram is the base unit, we
normally use grams in lab.

Mass in our class will be
measured using a digital
balances. They measure to the
nearest centigram, or 0.01 g.

We also have an analytical
balance, which measures to
0.001 g. It is really precise!
Volume Measurements

The units of volume we will use are mL and L because that is what
we measure in the lab. These are a type of “derived” unit, since they
are made up of base units.

V = l x w x h or (cm x cm x cm) = cm3

1.0 cm3 = 1.0 mL

Example: Convert 749 mL to liters

749 mL x
1 L
Yeah, this is important!
= 0.749 L
1000 mL
Can You Read the Volume Correctly?

What is the volume of
water in this cylinder?

Read the bottom of the
meniscus, estimate to
the nearest 0.1 mL

52.8 mL (+/- 0.1 mL)
Temperature Scales

Most people think that the
base temperature units of the
S.I. system are degrees
Celsius.

While it is true that Celsius is
the most commonly used unit,
the Celsius scale is actually
based on the Kelvin scale.
Kelvin is the base unit for
temperature.
William Thompson,
Lord Kelvin
•Degrees Kelvin are called
Kelvins, K
•No degree symbol is used for
K
•K is also called the “absolute
temperature scale”
•K = °C + 273
S.I. Prefixes

The best thing about the S.I. system is that it
is based on multiples of 10. The English
system is based on weird numbers like 16.
(Like there are 16 16ths in an inch…why?!)
There are many prefixes used to indicate the
size of S.I. units relative to each other. We
don’t need to learn them all, but several of
them are very common, and must be learned.
S.I. Prefixes To Know
Prefix
Factor
Symbol
mega
106
M
kilo
103
k
deci
10-1
d
centi
10-2
c
milli
10-3
m
micro
10-6
m
nano
10-9
n
S.I. Conversions

How do we use these prefixes? Why do we need to know this?

Example: Two students were given identical rulers and asked to
calculate the area of a piece of notebook paper. One student
measured the length of the paper as 28.0 cm. The other student
reported that the width of the paper was 216 mm. Before
multiplying these values to find the area, the units of each
measurement must be the same.


216 mm x 1 cm =
10 mm

A = l x w = 28.0 x 21.6 = 605 cm2
21.6 cm
Because a mm is 10 times smaller
than a centimeter.
Notice the conversion factor that
was used.
B. S. Rule (This stands for “brilliantly simple”, by the way)

There are many ways to remember how to convert from one unit to
another. Many students draw stair steps and know sayings about
King Henry.

Try learning the prefixes and using the B. S. Rule. Just draw an
arrow between B and S!

B  S When going from a big unit to a small unit, move the decimal
to the right.

B  S When going from small to big units, move the decimal to the
left.

Yeah, but how many places do I move it??
Number Line
If you think of the SI units as being on a
number line, you can just hop around.
|10-9
n
 Smaller
|10-6
µ
|10-3
m
|10-2 |10-1 |100 |101 |102 |103
c
d
↑
da
h
k
base
unit
|106
M
Bigger 
|109
G
Using the Prefixes

It’s easy to do conversions if you think of the prefixes as being on
a number line.

Example: Convert 458 nm to m

Find nm on the number line. Since it is way smaller than the m,
the decimal moves to the left nine places. B  S
0.000000458 m or in scientific notation 4.58 x 10-7
Dimensional Analysis




Dimensional analysis is a method of problem
solving that uses conversion factors, which
are written a fractions.
The fractions have numbers as well as units
The quantity in the numerator is equivalent to
the quantity in the denominator
Examples: 10 mm
60 s
1 min

1 cm
1 min
60 s
How do we do the math?

Most people are pretty comfortable multiplying fractions.

1 x 5 x 3 = 15
2 3
4
24
we just multiply the numerators together, and then the
the denominators. Then divide 15 by 24, which is 0.625
We can also use “Railroad Tracks” to make the calculation look neater:
1
2
|
|
5
3
|
|
3
4
=
15
24
= 0.625
Treat units the same way you treat numbers. They get multiplied and divided, too!
Example: cm x cm x cm = cm3
Example:
m3 = m
m2
Dimensional Analysis
Example: How many mm are in 147 km?
147 km x 1000 m x 1000 mm = 147,000,000 mm
1
1 km
1m
= 1.47 x 108 mm
Step 1: Start with what you are given.
Step 2: Multiply by a conversion factor that has the starting units in
the denominator, and the unit you want to find in the numerator.
(It may take more than one conversion factor to get to where you
want to go.)
Step 3: Multiply it out and then write in scientific notation
What about Scientific Notation Math?

When multiplying, add the exponents:
103 m x 104 m = 107 m2

When dividing, subtract the exponents
103 m = 10-1
104 m

OMG what if one of them is like, a negative?
103 m =
10-4 m
107
3-(-4) = 7
Using Dimensional Analysis to Solve
Problems

If you watched any of
the Olympics, you know
some amazing athletes
competed. Let’s look at
some of the new World
Records and see if we
can convert them to
everyday units, using
dimensional analysis
Swimming
Michael Phelps broke a World
Record and won a Gold Medal
by swimming the 100 m
Butterfly in 50.58 seconds.

What is this speed in feet per second? How ‘bout in miles per hour?

100 m x
50.58 s
3.28 ft
1m
6.48 ft x
1s
1 mile x 3600 s = 4.42 mi
5280 ft
1 hr
hr
=
6.48 ft
s
Metric to English conversion factors will be provided if you need them.
Swimming
Cesar studies at Auburn
University. (Great school.)


How does Michael’s phenomenal speed compare to another Gold
Medalist, Cesar Cielo of Brazil? Cesar swam the 50 m Freestyle
in 21.30 seconds.
50 m x
21.30 s
3.28 ft x 1 mi x 3600 s = 5.25 mi
1m
5280 ft
1 hr
hr
Wow, phaster than Phelps?
Track and Field

Speaking of fast, have you
seen this guy run?

Usain Bolt of Jamaica, won a
Gold Medal and broke Olympic
and World Records with his
time on the Men’s 200 meter.

Usain made it look easy as he
ran it in19.30 s.
Track and Field

Use dimensional analysis to find out Usain’s
speed in feet per second, and also in miles per
hour.
200 m x
19.30 s
3.28 ft
1m
=
40.0 ft
s
40.0 ft x 3600 s x 1 mi
=
s
1 hr
5280 ft
27.3 mi
hr
Accuracy vs. Precision


Accuracy refers to how
close a measured value is
to an accepted value. In
other words, “is it correct?”
The person practicing
archery in this photo was
not very accurate, only a
few of the arrows hit the
bull’s eye. They are not
very precise either, since
the arrows are all over the
place. (Random errors.)
This person needs glasses!
Precision

Precision has two general
meanings:

Precision refers to how close a
series of measurements are to
one another. In other words,
“is it repeatable?”

The word precision is also
used to indicate how exact a
measurement is. For example,
2.54 cm is more precise than
2.5 cm.

The target at right shows both
accuracy and precision.
This archer is accurate and
precise!
We need accuracy and precision…
World Champion Archer Joo
Hyun Jung from Korea says,
“You need both precision and
accuracy to win the GOLD!”
Significant Figures “Sig Figs”


If we want to measure things with accuracy and
precision, we must consider a topic known as
significant figures, a.k.a. significant digits.
Significant digits include all known digits plus
one estimated digit, for most measuring
instruments. Examples:




A large graduated cylinder can be read to the 0.1 mL
A buret can be read to the .01 mL
A digital balance does not have any estimated digits,
you just copy all the digits down.
Don’t drop final zeroes if they are to the right of the
decimal point!
Rules for Sig Figs- gotta know these 5
rules!

Rule Number One:
Non-zero numbers are
always significant.

Look at these examples:

You can see that we are
simply counting the
number of digits in these
measurements.
Measurement Number of
Significant
Digits
37.35 m
4
4563.9 s
5
198 °C
3
Sig Fig Rules

Rule Number Two:

Zeros between nonzero numbers are
always significant.

Look at these examples:

Again, you can see that
we are simply counting
all of the digits
Measurement Number of
Significant
Digits
203 g
3
1001 km
4
1000002 s
7
Sig Fig Rules


Rule Number Three: All
final zeros to the right of
the decimal point are
significant.
Measurement Number of
Significant
Digits
34.0 m
We are used to the idea that
4003.00 g
2.0 is the same thing as 2.
With measurements, this is
not true! The 2.0 is a more
accurate measurement.
1.000
3
6
4
Sig Figs


Measurement Number of
Significant
Digits
Rule Number Four: Zeros
that act as placeholders are
not significant. Convert
numbers to scientific
3000 m
notation to remove the
placeholder zeros.
(3 x 103)
See how converting to
scientific notation lets you
see how many digits to
count?
1
Only the 3 is significant
.0034 s
(3.4 x 10-2)
2
.0430 g
(4.30 x 10-2)
3
The “leading zeros” are
not significant.
Remember rule #3
says final zeros to the
right of the decimal are
significant.
Significant Figures


Rule Number Five:
Counting numbers and
defined constants have
an infinite number of
significant figures.
This just means that
these numbers do not
limit the precision of
your calculations.
Measurement Number of
Significant
Digits
29 students
Infinitely
exact
1000 mL = 1L
Here, 1000 has an
infinite no. of sig
figs since this is a
definition
2.54 cm = 1
inch
Same reason as
above
Calculations Involving Sig. Figs

There are two rules to keep in mind when doing calculations involving
significant figures.

When adding or subtracting measurements, your answer must have the
same number of digits to the right of the decimal point as the value with the
fewest digits to the right of the decimal point.

Example:
28.0 cm
23.538 cm
25.68 cm
+ 77.218 cm
Line up the decimals!
The answer can only go to the tenths place. The answer is 77.2 cm. (If the
sum had been 77.278 cm, the answer would have rounded up to 77.3 cm.)
Calculations Involving Sig. Figs.

The second rule is that when multiplying or dividing
measurements, your answer must have the same
number of significant figures as the measurement
with the fewest significant figures.

Example:
3.20 cm x 3.65 cm x 2.05 cm = 23.944 cm3
= 23.9 cm3
(since you can only have three sig figs, you must
round off to the tenth’s place.)