# Unit 1 Measurments PPT - TeacherWeb by fdshsdhs

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```									    Unit 1
Observation,
Measurement
and Calculations
Measurement

Measurement – a quantity that has both a
number and a unit.

• Measurements are fundamental to the experimental
sciences

• Units typically used in the sciences are the
International System of Measurements (SI)
Scientific Notation

In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000

In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Scientific Notation

Imagine the difficulty of calculating
the mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Scientific Notation:

A method of representing very large or
very small numbers in the form:
M x 10n

 M is a number between 1 and 10
 n is an integer
2 500 000 000           .
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x   109

The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5

Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x   10 -5

The exponent is negative
because the number we
started with was less
than 1.
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
Review:
Scientific notation expresses a
number in the form:
M x   10n
n is an
1  M  10          integer
4 x 106    IF the exponents are
+ 3 x 10 6   the same, we simply
add or subtract the
7 x 106    numbers in front and
bring the exponent
down unchanged.
The same holds true
4 x106
- 3 x10 6   for subtraction in
scientific notation.
1 x 106
4 x106    If the exponents are
+ 3 x 105   NOT the same, we
must move a decimal
to make them the
same.
4.00 x   10 4.00 x
6      10 6

+ 3.00 x 10 5 + .30 x 106

4.30 x 10 6
Move the
decimal on
the smaller
number!
A Problem for you…
2.37 x   10 -6

+ 3.48 x 10 -4
Solution…
2.37
002.37 x 10 -6

+ 3.48 x 10 -4
Solution…
0.0237 x 10 -4

+ 3.48   x 10 -4

3.5037 x 10 -4
Scientific Notation
Calculation Summary
You must express the numbers as the same power
of 10. This will often involve changing the decimal
place of the coefficient.
(2.0 x 106) + ( 3.0 x 107)
(0.20 x 107) + (3.0 x 107) = 3.20 x 107

(4.8 x 105) - ( 9.7 x 104)
(4.8 x 105) - ( 0.97 x 105) = 3.83 x 105
Scientific Notation
Multiplying
Multiply the coefficients and add the exponents
(xa) (xb) = x a + b
(2.0 x 106) ( 3.0 x 107) = 6.0 x 1013

Dividing
(xa) / (xb) = x a - b
(2.0 x 106) / ( 3.0 x 107) = 0.67 x 10-1
Divide the coefficients and subtract the exponents
Nature of Measurement
Measurement - quantitative observation
•
consisting of 2 parts

Part 1 - number
Part 2 - scale (unit)

Examples:
20 grams
6.63 x 10-34 Joule seconds
Uncertainty in Measurement

A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
Precision and Accuracy
Accuracy – measure of how close a measurement
comes to the actual or true value of whatever is
being measured.
Precision – measure of how close a series of
measurements are to one another.

Neither        Precise but not     Precise AND
accurate nor        accurate           accurate
precise
Why Is there Uncertainty?
 Measurements are performed with instruments
 No instrument can read to an infinite number of
decimal places
Which of these balances has the greatest
uncertainty in measurement?
Determining Error

Accepted Value – the correct
value based on reliable references

Experimental Value – the value
measured in the lab

Error(can be +or-)=experimental value – accepted value

Percent error = absolute value of error x 100%
accepted value
Significant Figures in
Measurement
In a supermarket, you can use the scales to
measure the weight of produce.

If you use a scale that is calibrated in 0.1 lb
intervals, you can easily read the scale to the
nearest tenth of a pound.

You can also estimate the weight to the nearest
hundredth of a pound by noting the position of the
pointer between calibration marks.
Significant Figures in
Measurement
If you estimate a weight that lies between 2.4 lbs
and 2.5 lbs to be 2.46 lbs, the number in this
estimated measurement has three digits.

The first two digits (2 and 4 ) are known with
certainty.

The rightmost digit (6) has been estimated and
involves some uncertainty.
Significant Figures in
Measurement
Significant figures in a measurement include all of
the digits that are know, 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.
Rules for Counting Significant
Figures

Nonzero integers always count as
significant figures.

3456 has
4 sig figs.
Rules for Counting Significant
Figures

Leading zeros do not count as
significant figures.

0.0486 has
3 sig figs.
Rules for Counting Significant
Figures

Zeros at the end of a number and
to the right of a decimal point are
always significant.
9.000 has
4 sig figs

1.010 has
4 sig figs
Rules for Counting Significant
Figures

Captive zeros always count as
significant figures.

16.07 has
4 sig figs.
Rules for Counting Significant
Figures
Zeros at the rightmost end that
lie at the left of an understood
decimal point are not significant.
7000 has
1 sig fig

27210 has
4 sig figs
Rules for Counting Significant
Figures
Exact numbers have an infinite
number of significant figures.

1 inch = 2.54 cm, exactly
Rules for Significant Figures in
Mathematical Operations

Multiplication and Division: # sig figs in
the result equals the number in the least
precise measurement used in the
calculation.

6.38 x 2.0 =
12.76  13 (2 sig figs)
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The number
of decimal places in the result equals the
number of decimal places in the least
precise measurement.

6.8 + 11.934 =
18.734  18.7 (3 sig figs)
Sig Fig Practice #1
How many significant figures in each of the following?

1.0070 m        5 sig figs
17.10 kg      4 sig figs

100,890 L        5 sig figs

3.29 x 103 s       3 sig figs
0.0054 cm         2 sig figs
3,200,000        2 sig figs
Sig Fig Practice #2
Calculation        Calculator says:     Answer
3.24 m x 7.0 m         22.68 m2            23 m2
100.0 g ÷ 23.7 cm3     4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2            0.05 cm2
710 m ÷ 3.0 s          236.6666667 m/s    240 m/s
1818.2 lb x 3.23 ft    5872.786 lb·ft     5870 lb·ft
1.030 g ÷ 2.87 mL      2.9561 g/mL       2.96 g/mL
Sig Fig Practice #3
Calculation        Calculator says:   Answer
3.24 m + 7.0 m           10.24 m         10.2 m
100.0 g - 23.73 g         76.27 g        76.3 g
0.02 cm + 2.371 cm        2.391 cm       2.39 cm
713.1 L - 3.872 L         709.228 L      709.2 L
1818.2 lb + 3.37 lb       1821.57 lb     1821.6 lb
2.030 mL - 1.870 mL       0.16 mL        0.160 mL
Questions
1) 78ºC, 76ºC, 75ºC 2) 77ºC, 78ºC, 78ºC
3) 80ºC, 81ºC, 82ºC
The sets of measurements were made of the boiling
point of a liquid under similar conditions. Which
set is the most precise?
Set 2 – the three measurements are closest together.
What would have to be known to determine which set
is the most accurate?
The accepted value of the liquid’s boiling point
Questions
How do measurements relate to experimental
science?

Making correct measurements is fundamental to the
experimental sciences.
How are accuracy and precision evaluated?
Accuracy is the measured value compared to the
correct values. Precision is comparing more than
one measurement.
Questions
Why must a given measurement always be reported to the
correct number of significant figures?

The significant figures in a calculated answer often depend on
the number of significant figures of the measurements
used in the calculation.

How does the precision of a calculated answer compare to the
precision of the measurements used to obtain it?

A calculated answer cannot be more precise than the least
precise measurement used in the calculation.
Question
A technician experimentally determined the boiling
point of octane to be 124.1ºC. The actual boiling
point of octane is 125.7ºC. Calculate the error and
the percent error.

Error = experimental value – accepted value
error = 124.1ºC – 125.7ºC = -1.6ºC
Absolute error / accepted value x 100%
% error = -1.6ºC / 125.7ºC x 100% = 1.3%
Question
Determine the number of significant figures in each of
the following
11 soccer player
unlimited
0.070 020 meter
5
10,800 meters
3
5.00 cubic meters
3
Question
Solve the following and express each answer in scientific
notation and to the correct number of significant figures.

(5.3 x 104) + (1.3 x 104)
6.6 x 104
(7.2 x 10-4) / (1.8 x 103)
4.0 x 10-7
(104)(10-3) (106)
107
(9.12 x 10-1) - (4.7 x 10-2)
8.65 x 10-1
(5.4 x 104) (3.5 x 109)
18.9 x 1013 or 1.9 x 10 14
Don’t be scared!
International Systems of Units
• The standards of measurement used in science
are those of the metric system
• All metric units are based on multiples of 10
• Metric system was originally establish in France
in 1795
• The International System of Units (SI) is a
revised version of the metric system.
• The SI comes from the French name, le
Systeme International d’Unites.
• The SI was adopted by international agreement
in 1960.
International Systems of Units
There are seven SI base units
SI Base Units
Quantity          SI base unit     Symbol
Length                   Meter             m
Mass                    kilogram           kg
Temperature              kelvin             K
Time                    second              s
Amount                   mole              mol
Luminous intensity      candela            cd
Electric current        ampere              A
Metric Prefixes
Mega (M)
Kilo (k) 103
Hecto (hm) 102
Deka(da) 101
Meter (m)

left                       Deci (d) 10-1
Centi (c) 10-2
Milli (m) 10-3
right                                      Micro (µ) 10-6
Nano (nm) 10-9
Pico (pm) 10-12
Metric Conversions
1.0 decimeter (dm) = ? hectometers
0.001 hectometer (hm)
2.5 hectometer (hm) = ? millimeters
250,000 millimeters (mm)
9.7 centimeters (cm) = ? kiometers
0.000097 kilometers (km)
7.4 grams (g) = ? Milligrams (mg)
7400 milligrams (mg)
Other Common Conversions
1 cm3 = 1ml
1dm3 = 1L
1 inch = 2.54 cm
1kg = 2.21 lb
454 g = 1 lb
4.18 J = 1 cal
1 mol = 6.02 x 1023 pieces
1 GA = 3.79 L
Units of Length
meter – the basic SI unit of length or linear measure

Common metric units of length include the centimeter
(cm), meter (m), and kilometer (km)
Units of Volume
Volume -the space occupied by any sample of matter
Volume (cube or rectangle) = length x width x height
The SI unit of volume is the amount of space occupied
by a cube that is 1m along each edge. (m3)
Liter (L) – non SI unit – the volume of a cube that is
10cm along each edge (1000cm3)
The units milliliter and cubic centimeter are used
interchangeably.
1 cm3 = 1ml
1dm3 = 1L
Units of Mass
Common metric units of mass include the
kilogram, gram, milligram and microgram.
Weight – is a force that measures the pull on a
given mass by gravity.

Weight is a measure of force and is different than
mass.
Mass – measure of the quantity of matter.
Although, the weight of an object can change with
its location, its mass remains constant
regardless of its location.
Objects can become weightless, but not massless
Units of Temperature
Temperature – measure of how hot or cold an
object is.
The objects temperature determines the direction
of heat transfer.
When two objects at different temperatures are in
contact, heat moves from the object at the
higher temperature to the object at the lower
temperature.
Scientist use two equivalent units of temperature,
the degree Celsius and the Kelvin.
Units of Temperature
The Celsius scale of the metric system is named after
Swedish astronomer Anders Celsius.
The Celsius scale sets the freezing point of water at
0ºC and the boiling point of water at 100ºC
The Kelvin scale is named for Lord Kelvin, a Scottish
physicist and mathematician.
On the Kelvin scale, the freezing point of water is
273.15 kelvins (K), & the boiling point is 373.15 K.
With the Kelvin scale the degree (º) sign is not used
Units of Temperature
A change of 1 º on the Celsius scale is equivalent to
one kelvin on the Kelvin scale.

The zero point on the Kelvin scale, 0K, or absolute
zero, is equal to -273.15º C.

K = ºC + 273

ºC = K - 273
.
Units of Energy
Energy – the capacity to do work or to produce heat.
The joule and the calorie are common units of
energy.
The joule (J) is the SI unit of energy named after the
English physicist James Prescott Joule.
1 calorie (cal) - is the quanity of heat that raises the
temperature of 1 g of pure water by 1ºC.
1 J = 0.2390 cal

1 cal = 4.184 J
End of Section 3.2
Conversion Factors
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies

Different ways to express the same amount of money

1 meter =10 decimeters =100 centimeters =1000 millimeters

Different ways to express length
Whenever two measurements are equivalent, a ratio
of the two measurements will equal 1.
1 m = 100 cm = 1
1m
Conversion factor
Conversion Factors
Conversion factor – a ratio of equivalent
measurements
100 cm / 1 m
1000 mm / 1 m
The measurement on the top is equivalent to the
measurement on the bottom
Read “one hundred centimeters per meter” and “1000
millimeters per meter”
Smaller number        1m             larger unit
Larger number        100 cm         smaller unit
Conversion Factors
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.
Conversion factors within a system of measurements
are defined quantities or exact quantities.
Therefore, they have an unlimited number of
significant figures and do not affect the rounding of

How many significant figures does a conversion
factor within a system of measurements have?
Dimensional Analysis
Dimensional analysis – a way to analyze and solve
problems using the units, or dimensions, of the
measurements.
How many minutes are there in exactly one week?
60 minutes = 1 hour         24 hours = 1 day
7 days = 1 week

1 week 7 days 24 hours    60 minutes = 10,080 min
1 week   1 day       1 hour

1.0080 x 104 min
Dimensional Analysis
How many seconds are in exactly a 40-hr work
week?

60 minutes = 1 hour        24 hours = 1 day
7 days = 1 week            60 seconds = 1 minute

40 hr 60 min 60 sec   = 144,000 s
1 hr   1 min

1.44000 x 105 s
Dimensional Analysis
An experiment requires that each student use an
8.5 cm length of Mg ribbon. How many students
can do the experiment if there is a 570 cm length of
Mg ribbon available?

570 cm ribbon    1 student       = 67 students
8.5 cm ribbon

2 sig figs
Dimensional Analysis
A 1.00º increase on the Celsius scale is equivalent to a
1.80º increase on the Fahrenheit scale. If a temperature
increases by 48.0ºC, what is the corresponding
temperature increase on the Fahrenheit scale?

48.0ºC      1.80ºF = 86.4ºF
1.00ºC

A chicken needs to be cooked 20 minutes for each
pound it weights. How long should the chicken be
cooked if it weighs 4.5 pounds?
4.5 lb 20 min     = 90 min
lb
Dimensional Analysis
Gold has a density of 19.3 g/cm3. What is the density in
kg/m3

19.3 g 1 kg       1 x 106 cm3 = 1.93 x 104 kg / m3
cm3 1000 g        m3

There are 7.0 x 106 red blood cell (RBC) in 1.0 mm3
of blood. How many red blood cells are in 1.0 L of
blood?
7.0 x 106 RBC     1 x 106 mm3 1 dm3 = 7.0 x 1012
1.0 mm3              dm3        1L
Dimensional Analysis
1.00 L of neon gas contains 2.69 x 1022 neon atoms. How
many neon atoms are in 1.00mm3 of neon gas under the
same conditions?

2.69 x 1022 atoms    1L      dm3
1.00 L            1 dm3    1 x 106 mm3

2.69 x 1016 atoms in 1.00mm3 of gas
Questions
What conversion factor would you use to convert between
these pairs of units?

Minutes to hours
1 hour / 60 minutes

grams to milligrams
1000 mg / 1 g

Cubic decimeters to milliliters
1000 ml / 1 dm3
Questions
An atom of gold has a mass of 3.271 x 10-22g. How many
atoms of gold are in 5.00 g of gold?

1.53 x 1022 atoms of gold
Light travels at a speed of 3.00 x 1010 cm/sec. What
is the speed of light in km/hour?

1.08 x 109 km/hr
Questions
Convert the following. Express your answers in scientific
notation.

7.5 x 104 J to kJ
7.5 x 101 kJ

3.9 x 105 mg to dg
3.9 x 103dg

2.21 x 10-4 dL to µL
2.21 x 101µL
Questions
Make the following conversions. Express your answers in
standard exponential form.

14.8 g to µg
1.48 x 107 µg

3.75 x 10-3 kg to g
3.72 g

66.3 L to cm3
6.63 x 104 cm3
Density
If a piece of led and a feather of the same volume are
weighted, the lead would have a greater mass than the
feather.
It would take a much larger volume of feather to equal
the mass of a given volume of lead.
Density = mass / volume
D=m/v
Mass is a extensive property (a property that depends on
the size of the sample)

Density is an intensive property (depends on the
composition of a substance, not on the size of the sample)
Density
A helium filled balloon rapidly rises to the ceiling when
released.

Whether a gas-filled balloon will sink or rise when
released depends on how the density of the gas
compares with the density of air.

Helium is less dense than air, so a helium filled
balloon rises.
Density and Temperature
The volume of most substances increase as the
temperature increases.
The mass remains the same despite the temperature
and volume changes.
So if the volume changes with temperature while the
mass remains constant, then the density must also
change with temperature.
The density of a substance generally decreases as its
temperature increases. (water is the exception: ice floats
because it is less dense than liquid water)
Questions
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 245cm3 and a mass of 612g.
Was is the density? Is it aluminum?
D = 612g / 245cm3 = 2.50g/cm3
D of aluminum is 2.70 g/cm3; no it is not aluminum
A bar of silver has a mass of 68.0 g and a volume of
6.48 cm3. What is the density?

D = 68.0g / 6.48 cm3 = 10.5 g/cm3
Questions
The density of boron is 2.34 g/cm3. Change 14.8 g of
boron to cm3 of boron.
D = m / v or v = m / D
V = 14.8 g    cm3 = 6.32 cm 3
2.34 g

Convert 4.62 g of mercury to cm3 by using the density
of mercury -13.5 g/cm3.

V = 46.2 g     cm3 = 0.342 cm 3
13.5 g
Density

D=m/v

v=m/D

m=D·v
The End

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