Units of Measurements
2. Conversion Problems
3. Density
Measurements and their Uncertainty
1.
4.
Do any of these signs
list a measurement?
- Measurements
contain BOTH a
number and a unit.


All measurements depend on units that
serve as reference standards. The standards
of measurement used in science are those
of the metric system.
 Based on multiples of 10
The International System of Units
(abbreviated SI, after the French name, Le
Système International d’Unités) is a revised
version of the metric system.


What do the SI prefixes deci, centi, and milli
mean?
Think about the word decimal, century, and
millennium.
What metric units are commonly used
to measure length, volume, mass,
temperature and energy?


In SI, the basic unit of length, or linear measure, is
the meter (m).
For very large or and very small lengths, it may be
more convenient to use a unit of length that has a
prefix.
Volume - space occupied by any sample of
matter
How do you calculate the volume of a cube?
The SI unit of volume is the amount of space occupied
by a cube that is 1 m along each edge. This volume is
the cubic meter (m)3
“I’ll have a liter of cola”
What unit of volume are you
most familiar with?


The liter is a NON SI unit of measurement!
A liter (L) is the volume of a cube that is 10
centimeters (10 cm) along each edge (10 cm  10
cm  10 cm = 1000 cm3 = 1 L).

Common quantities
The volume of 20 drops of
liquid from a medicine dropper
is approximately 1 mL.
A sugar cube has a volume of 1
cm3. 1 mL is the same as 1 cm3.

The mass of an object is measured in comparison
to a standard mass of 1 kilogram (kg), which is the
basic SI unit of mass.
Common metric units of mass include
kilogram, gram, milligram, and microgram.

How does weight
differ from mass?
Weight is a force that measures the pull on
a given mass by gravity.
Mass is a measure of the quantity of
matter. (the space it occupies)
Temperature
-
is a measure of how hot or cold
an object is.
Thermometers are used to measure temperature.
• Substances expand with an
increase in temperature.
When 2 objects at different
temperatures are in contact,
heat travels from:
Lower
temperature
Higher
temperature
Scientists commonly use two equivalent units of
temperature, the degree Celsius and the Kelvin.
Celsius
Reference points
Kelvin
Fahrenheit

The zero point on the Kelvin scale, 0 K, or absolute
zero, is equal to 273.15 °C.

Because one degree on the Celsius scale is
equivalent to one Kelvin on the Kelvin scale,
converting from one temperature to another is
easy. You simply add or subtract 273, as shown in
the following equations.
Converting Between Temperature Scales
Normal human body temperature is 37C. What is that
temperatures in kelvins?
Analyze: List the known and the unknown.
Known
◦ Temperature in C = 37C
Unknown
◦ Temperature in K = ?K
Equation: K= C + 273
Calculate: Solve for the unknown.
K= C + 273
37 + 273 = 310K
Liquid nitrogen boils at 77.2 K. What is this
temperature in degrees Celsius?
Analyze: List the known and the unknown.
Calculate: Solve for the unknown.
-196C
1 J = 0.2390 cal
1 cal= 4.184 J
Energy - the capacity to do work or to produce heat.
The joule and the calorie are common units of
energy.


Joule (J) is the SI unit of energy.
1 calorie (cal) is the quantity of heat that raises the
temperature of 1g of pure H2O by 1C.
1. Which of the following is not a base SI
unit?
A. meter
B. gram
C. second
D. mole

2. If you measured both the mass and weight of an
object on Earth and on the moon, you would find
that
A. both the mass and the weight do not change.
B. both the mass and the weight change.
C. the mass remains the same, but the weight
changes.
D. the mass changes, but the weight remains the
same.
3. A temperature of 30 degrees Celsius is
equivalent to
A. 303 K.
B. 300 K.
C. 243 K.
D. 247 K.
K = C + 273

Can you think of any other examples in which
quantities can be expressed in several
different ways?

Consider the conversion units of distance:
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
When 2 measurements are equivalent, a ratio of
the 2 measurements equals 1
or
Conversion factor
Remember: even though the numbers in the
measurements 1 m and 100 cm differ, both
measurements represent the same length
What happens when a measurement is
multiplied by a conversion factor?

When a measurement is multiplied by a conversion
factor, the numerical value is generally changed,
but the actual size of the quantity measured
remains the same.
3.
3


A conversion factor is a ratio of equivalent
measurements.
The ratios 100 cm/1 m and 1 m/100 cm are
examples of conversion factors.
Fig. 3.11
3.
3

The scale of the micrograph is in nanometers.
Using the relationship 109 nm = 1 m, you can write
the following conversion factors.
Dimensional analysis is a way to analyze and solve
problems using the units, or dimensions, of the
measurements.


Why is dimensional analysis useful?
An alterative way to problem solving
Sample Problem 3.5
How many seconds are in a workday that lasts
exactly eight hours?
Analyze: List the knowns and the unknown.
Known
◦ Time worked = 8 h
◦ 1 hour = 60 min
◦ 1 minute = 60 s
Unknown
◦ Seconds worked = ? s
Calculate: Solve for the unknown.
1.) How many minutes are there in exactly one
week?
Analyze: List the knowns and the unknown.
Known
Unknown
1.0080x104min
Calculate: Solve for the unknown.
2.) How many seconds are in exactly a 40-hour work
week?
Analyze: List the knowns and the unknown.
Known
Unknown
Calculate: Solve for the unknown.
1.44000x105s
1.) The directions for an experiment ask each
student to measure 1.84g of copper (Cu)
wire. The only copper wire available is a
spool with a mass of 50.0g. How many
students can do the experiment before the
copper runs out?
27 students
2.) A 1.00-degree increase on the Celsius scale
is equivalent to a 1.80-degree increase on
the Fahrenheit scale. If a temperature
increase by 48.0C, what is the corresponding
temperature increase on the Fahrenheit scale?
86.4 F
What types of problems are easily solved by
using dimensional analysis?

Problems in which a measurement with one unit is
converted to an equivalent measurement with
another unit are easily solved using dimensional
analysis.
Express 750 dg in grams.
Analyze: List the knowns and the unknown.
Known
Mass = 750 dg
1 g = 10 dg
Unknown
Mass = ? g
Calculate: Solve for the unknown.
Conversion
unit
Convert the following.
cm3
to liters
1.5 x 10-2L
a)
15
b)
7.38 g to kilograms
c)
6.7 s to milliseconds 6.7 x 103ms
d)
94.5 g to micrograms 9.45 x 107g
7.38 x 10-3kg
Entertainment & Chemistry
Learning Network
Purpose: to use dimensional analysis to convert
between English and metric units.
Procedure: Using the player stats for the New
England Patriots, convert heights and weights
into heights and masses expressed in meters
and kilograms, respectively.
 You must document your approach:
◦ Identify the known, unknown, and conversion
factor.
◦ Must show all calculations.
2.54 cm = 1 inch
454g = 1 lb
What is 0.073 cm in micrometers?
Analyze: List the knowns and the unknown.
Known
Length = 0.073 cm = 7.3x10-2 cm
102 cm = 1m
1m = 106 m
Unknown
Length = ? m
Calculate: Solve for the unknown.
1.
The radius of a potassium
atom is 0.227nm. Express the
radius to the unit centimeters.
2.27 x 10-8 cm
2.
The diameter of Earth is 1.3 x
104km. What is the diameter
expressed in decimeters?
1.3 x 108 dm
The mass per unit volume of a substance is a property
called density. The density of manganese, a metallic
element, is 7.21 g/cm3. What is the density of
manganese expressed in units kg/m3?
Analyze: List the knowns and the unknown.
Known
Density of manganese = 7.21 g/cm3
103 g = 1kg
106cm3 = 1m3
Unknown
Density manganese = ? kg/m3
Density of manganese = 7.21 g/cm3
103 g = 1kg
106cm3 = 1m3
g/cm3
kg/m3
Calculate: Solve for the unknown.
7.21 x 103 kg/m3
1.
Gold has a density of 19.3 g/cm3. What is the
density in kilograms per cubic meter?
g/cm3
103 g = 1 kg
106 cm3 = 1 m3
2.
1.93 x 104 kg/m3
There are 7.0 x 106 red blood cells (RBC) in 1.0
mm3 of blood. How many red blood cells are in
1.0 L of blood?
mm3 = 1 m3
106 cm3 = 1 m3
1cm3 = 1 mL
103mL = 1 L
7.0 x 1012 RBC/L
1 Mg = 1000 kg. Which of the following would
be a correct conversion factor for this
relationship?
A.  1000.
B.  1/1000.
C. ÷ 1000.
D. 1000 kg/1Mg.
The conversion factor used to convert joules to calories
changes
A. the quantity of energy measured but not the numerical
value of the measurement.
B.
neither the numerical value of the measurement nor the
quantity of energy measured.
C. the numerical value of the measurement but not the
quantity of energy measured.
D. both the numerical value of the measurement and the
quantity of energy measured.
How many  g are in 0.0134 g?
A. 1.34  10–4
B. 1.34  10–6
C. 1.34  106
D. 1.34  104
Express the density 5.6 g/cm3 in kg/m3.
A. 5.6  106kg/m3
B. 5.6  103kg/m3
C. 0.56 kg/m3
D. 0.0056 kg/m3
Which is heavier, a pound of lead or a
pound of feathers?

Why can boats made of steel float on water
when a bar of steel sinks?
What determines the density of a substance?
Density is the ratio of the mass of an object to its
volume.

Each of these 10-g samples has a different volume
because the densities vary.
Which substance has
the highest ratio of
mass to volume?
Date: 10/11/2012
1.
2.
3.
Define what an intensive property is.
Provide 3 examples of an intensive
property.
Provide 2 examples of an extensive
property.

Density is an intensive property that depends
only on the composition of a substance, not on
the size of the sample.
For example, a 10.0-cm3 piece of lead has a
mass of 114 g. What is the density of lead?
Unit of density: g/cm3

What would happen if corn oil is poured into
a glass containing corn syrup?
OIL
SYRUP

Simulation 1
◦ Rank materials according to their densities.
ChemASAP/dswmedia/rsc/asap1_chem05_cmsm0301.html




Volume
as temperature
The mass remains the same despite the
temperature and volume changes.
Recall:
If volume changes with
temperature and mass stays the
same, then density must change.
The density of a substance generally
decreases as its temperature
increases.
100 F
DENSITY
TEMPERATURE
50 F
0 F
A copper penny has a mass of 3.1 g and a
volume of 0.35 cm3. What is the density of
copper?
Analyze: List the knowns and the unknown.
Known
Mass = 3.1 g
Volume = 0.35 cm3
Unknown
Density = ? g/cm3
8.8571 g/cm3
1.
A student finds a shiny piece of metal that
she thinks is aluminum. In the lab, she
determines that the metal has a volume of
245 cm3 and a mass of 612g. Calculate the
density. Is the metal aluminum?
2.50 g/cm3 - NO
2.
A bar of silver has a mass of 68.0g and a
volume 6.48 cm3. What is the density of
silver?
10.5 g/cm3
What is the volume of a pure silver coin that
has a mass of 14 g? The density of silver (Ag)
is 10.5 g/cm3.
Analyze: List the knowns and the unknown.
Known
Mass of coin = 14 g
Density of silver = 10.5 g/cm3
Unknown
volume of coin= ? cm3
1.3 cm3 of Ag
1.
Use dimensional analysis and the given densities
to make the following conversions.
a. 14.8 g of boron to cm3 of boron. The density
of boron is 2.34 g/cm3.
Volume of B = 6.32 cm3
b. 4.62 g of mercury to cm3 of mercury. The
density of mercury is 13.5 g/cm3.
Volume of Hg = 0.342 cm3
2.
Rework the preceding problems by applying the
following equation.
Make the following conversions:
1.
2.53 cm3 of gold to grams
(density of gold = 19.3 g/cm3)
48.8 g
2.
1.6 g of oxygen to liters
(density of oxygen = 1.33 g/L)
1.2 L
3.
25.0 g of ice to cubic centimeters
(density of ice = 0.917 g/cm3)
27.3 cm3
If 50.0 mL of corn syrup have a mass of 68.7
g, the density of the corn syrup is
a. 0.737 g/mL.
b. 0.727 g/mL.
c. 1.36 g/mL.
d. 1.37 g/mL.
What is the volume of a pure gold coin that has a
mass of 38.6 g? The density of gold is 19.3
g/cm3.
a. 0.500 cm3
b. 2.00 cm3
c. 38.6 cm3
d. 745 cm3
As the temperature increases, the density of
most substances
a. increases.
b. decreases.
c. remains the same.
d. increases at first and then decreases.

Today’s current weather in Eastville is

The Weather Channel projected forcast:

Eastern Shore News
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What everyday activities involve
measuring?
Recall which units of measure are related to
each of the examples you provide.
Estimate how tall you are in inches.
Have your lab partner estimate how tall
you are with a yard stick.
Compare the estimates with the yard
stick value.
A measurement is a quantity that has both a number
and a unit.
Ex.
Height
 Cooking
 Speed
Weight
Measurements are fundamental to the
experimental sciences. For that reason, it is
important to be able to make measurements
and to decide whether a measurement is
correct.
In scientific notation, a
given number is written
as the product of two
numbers: a coefficient
and 10 raised to a
power.
Example:
602,000,000,000,000,000,000,000
Scientific notation = 6.02x1023
3.
1


Accuracy - a measure of how close a
measurement comes to the actual or true
value of whatever is measured.
Precision - a measure of how close a series
of measurements are to one another.

To evaluate the accuracy of a measurement, the
measured value must be compared to the correct
value.

To evaluate the precision of a measurement, you
must compare the values of two or more
repeated measurements.
3.
1
Determining Error
Suppose you are using a thermometer to measure
the boiling point of pure H2O at STP. The
thermometer reads 99.1C. The true, or accepted
value of the boiling point of pure H2O under these
conditions (STP) is actually 100 C.
 Which is the accepted value?
 Which is the experimental value?
 What is the error?



The accepted value is the correct value based on
reliable references.
The experimental value is the value measured in
the lab.
The difference between the experimental value and
the accepted value is called the error.
• Error can be positive or negative depending on whether the
experimental value is greater than or less than the accepted
value.
The percent error is the absolute value of the error
divided by the accepted value, multiplied by 100%.
Suppose you are using a thermometer to measure
the boiling point of pure H2O at STP. The
thermometer reads 99.1C. The true, or accepted
value of the boiling point of pure H2O under these
conditions (STP) is actually 100 C.

Just because a measuring device works, you cannot
assume it is accurate. The scale below has not been
properly zeroed, so the reading obtained for the
person’s weight is inaccurate.
Suppose you estimate a weight that is between 2.4 lb
and 2.5 lb to be 2.46 lb. The first two digits (2 and
4) are known. The last digit (6) is an estimate and
involves some uncertainty. All three digits convey
useful information, however, and are called
significant figures.
The significant figures in a measurement include all
of the digits that are known, plus a last digit that is
estimated.
Measurements MUST ALWAYS be reported to the
correct number of significant figures because
calculated answers often depend on the
number of significant figures in the values
used in the calculation.
Animation
See how the precision of a calculated result depends
on the sensitivity of the measuring instruments.
3.
1
How many significant figures are in each
measurement?
1.
123 m
2.
40.506 mm 5 sig figs (rule 2)
3.
9.8000 x 104 m 5 sig figs (rule 4)
4.
22 meter sticks Unlimited (rule 6)
5.
0.07080 m 4 sig figs (rule 2, 3,4 )
6.
98,000 m 2 sig figs (rule 5)
3 sig figs (rule 1)
1.
How many significant figures are in each length?
a. 0.05730 meters
4 sig figs
b. 8765 meters 4 sig figs
c. 0.00073 meters 2 sig figs
d. 40.007 meters 5 sig figs
2.
How many significant figures are in each
measurement?
a. 143 grams 3 sig figs
b. 0.074 meter 2 sig figs
c. 8.750 x 10-2 gram 4 sig figs
d. 1.072 meter 4 sig figs

How does the precision of a calculated
answer compare to the precision of the
measurements used to obtain it?
3.
1
In general, a calculated answer cannot be
more precise than the least precise
measurement from which it was
calculated.

The calculated value must be rounded
to make it consistent with the
measurements from which it was
calculated.
To round a number, you must first decide how many
significant figures your answer should have. The
answer depends on the given measurements and
on the mathematical process used to arrive at the
answer.
 If the digit immediately to the right of the last significant digit
is less than 5, it is simply dropped and the value of the last
significant digit stays the same.
2.691 m  2.69 m
 If the digit in question is 5 or greater, the value of the digit in
the last significant place is increased by 1
294.8 mL  295 mL
Round off each measurement to the number of
significant figures shown in parentheses. Write the
answer in scientific notation.
1.
314.721 meters (4)
2.
0.001775 meter (2)
3.
8792 meters (2)
Round each measurement to three significant
figures. Write your answers in scientific notation.
8.71 x 101 m
1.
87.073 meters
2.
4.3621 x 108 meters 4.36 x 108 m
3.
0.01552 meter
4.
9009 meters
5.
1.7777 x 10-3 meter 1.78 x 10-3 m
6.
629.55 meters 6.30 x 102 m
1.55 x 10-2 m
9.01 x 103 m


The answer to an addition or subtraction calculation
should be rounded to the same number of decimal
places (not digits) as the measurement with the least
number of decimal places.
Example:
12.52 meters + 349.0 meters + 8.24 meters
Step 1 – align the decimal points and identify least # of
decimal places.
12.52 meters - 2 decimal places
349.0 meters - 1 decimal places
+ 8.24 meters - 2 decimal places
369.76 meters  369.8 meters
or 3.698 x 102 meters
Perform each operation. Express your answers to the
correct number of significant figures.
1.
61.2 meters + 9.35 meters + 8.6 meters
79.2 m
2.
9.44 meters – 2.11 meters
7.33 m
3.
1.36 meters + 10.17 meters
11.53 m
4.
34.61 meters – 17.3 meters
17.3 m

In calculations involving multiplication and
division, you need to round the answer to the
same number of significant figures as the
measurement with the least number of
significant figures.

The position of the decimal point has nothing
to do with the rounding process when
multiplying and dividing measurements.
Step 1 – determine # of sig figs
Step 2 – calculate answer
Step 3 – determine answer w/ correct # of sig figs.
Perform the following operations. Give the answers
to the correct number of significant figures.
1.
2.
(2)
(3)
7.55 meters x 0.34 meter = 2.576 (meter)2
2.6 m2
(3)
(2)
2.10 meters x 0.70 meter = 1.47 (meter)2
1.5 m2
3.
(5)
(2)
2.4526 meters ÷ 8.4 = 0.291976 meter
0.29 m
1.
In which of the following expressions is the
number on the left NOT equal to the number on
the right?
a. 0.00456  10–8 = 4.56  10–11
b. 454  10–8 = 4.54  10–6
c. 842.6  104 = 8.426  106
d. 0.00452  106 = 4.52  109
2.
Which set of measurements of a 2.00-g standard
is the most precise?
a. 2.00 g, 2.01 g, 1.98 g
b. 2.10 g, 2.00 g, 2.20 g
c. 2.02 g, 2.03 g, 2.04 g
d. 1.50 g, 2.00 g, 2.50 g
3.
A student reports the volume of a liquid as
0.0130 L. How many significant figures are in this
measurement?
a. 2
b. 3
c. 4
d. 5