Download scientific notation

Chapter 5
Measurements and
Calculations
1
Scientific Measurements
In science we have two types of observations:
Qualitative: observations of color, odor,
appearance, etc.
Quantitative: observations of measurement.
2
Scientific Measurements
Scientific measurements must always be represented as a
number and a unit.
During a lab, if units are not included, or improperly
included, it could result in drastically different results.
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Scientific Notation
When using scientific notation for very large numbers:
1. Move the decimal to the left until there is only
one digit between 1 and 10.
2. Count the number of places you move the
decimal and make this the power of 10.
3. Rewrite your number as a decimal times 10 to the
power of x. X= the number of places you moved the
decimal.
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Scientific Notation
EXAMPLE:
930
1. Move the decimal to make the number
between 1 and 10.
930 => 9.30
2. Multiply by 10 raised to a power of 2,
because the decimal was moved 2 places.
9.3x 102
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Scientific Notation
When a very small number is involved, the decimal
must be moved to the right instead of the left, in this
case we make the power of 10 a negative number.
0.0000093 => move the decimal 6 places to the right.
9.3 x 10-6
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Scientific Notation
EXAMPLES:
Convert to scientific notation:
1. 8,000
2. 75,600,000,000
3. 0.000000546
4. 0.0004876
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Scientific Notation
Multiplication and Division of Scientific Notation:
When multiplying 2 numbers with exponents, you must
add the exponents.
EXAMPLE: (3.2 x 104)(2.8 x 103)=
(3.2 x 2.8) x 104+3= 9.0 x 107
When dividing you subtract the exponents.
EXAMPLE: 6.4 x 103
= 6.4/8.3 x 103-5
8.3 x 105
=0.77 x 10-2 = 7.7 x 10-3
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Scientific Notation
Addition and subtraction of scientific notation
requires that all the numbers are raised to the
same power of 10
EXAMPLE:
1.31 x 105 + 4.2 x 104 =
13.1 x 104 + 4.2 x 104 =(13.1 + 4.2) x 104
= 17.3 x 104 = 1.73 x 105
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Dimensional Analysis
In order to solve this problem and many others in
chemistry we are going to use a process called
dimensional analysis. We are going to analyze the
dimensions or units involved here.
First we must figure out the conversion factors. These
are the numbers that help us convert from one unit
to another.
1 dozen = ? cookies
1 package = ? cookies
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Dimensional Analysis
So the conversion factor for the first is
1 dozen = 12 cookies, also if we read the problem we
can learn that
1 package = 6 cookies
We can now use this information to calculate how many
packages we need.
3 dozen x 12 cookies x 1 package = 6 pkgs.
1
1 dozen
6 cookies
We can cancel units that are the top and bottom of the
equation because this equals 1.
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Dimensional Analysis
If you divide 2 this equals 1. The same rule
2
applies when dividing units. Cookies = 1
cookies
Or elephants = 1
elephants
It does not matter what the unit is, if it is on the
top and bottom of the equation, they equal 1.
And anything times one is anything. 2x1= 2 or
cookies x 1 = cookies
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Dimensional Analysis
So let’s look at our problem again.
3 dozen x 12 cookies x 1 package = 6 pkgs.
1
1 dozen
6 cookies
The dozen cancels, the cookies cancel and we are left
with only packages as a unit.
IT IS VERY IMPORTANT TO ALWAYS CLEARLY WRITE
DOWN YOUR UNITS!!!
If you do not, you WILL lose track and your answer will
become incorrect.
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Dimensional Analysis
Earlier we measured the length of a pin. We found this
pin to be 2.85 cm, how many inches is this? There
are 2.54 cm in 1 inch.
1. Before we start the problem, read carefully and find
what we piece of information we are trying to
calculate here.
How many inches is the pin?
2. Then write down the information you are given.
The pin is 2.85 cm and 2.54 cm = 1 in.
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Dimensional Analysis
Now we can set up our problem.
3. Always start with the given value, in this case it would
be 2.85 cm.
2.85 cm x 1 inch = ?
1
2.54 cm
4. Next write in your conversion factor(s).
5. Now check your units and see if they cancel.
If they don’t….then you need to find the missing units.
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Dimensional Analysis
6. Draw a light line through your canceled units.
2.85 cm x 1 inch = 1.12 inches
1
2.54 cm
7. Multiply and divide you answer and add your final
units to your answer.
8. Check your significant figures.
9. Ask whether your answer makes sense.
16
Dimensional Analysis
1. The length of a marathon race is
approximately 26.2 miles. What is this
distance in kilometers?
HINT: 1 mi = 1760 yd and 1 m = 1.094 yd
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Dimensional Analysis
Your set up:
26.2 mi x 1760 yd x 1 m =
1
1 mi
1.094 yd
Do the units cancel?
What units is the answer supposed to be in?
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Dimensional Analysis
26.2 mi x 1760 yd x 1 m
x 1km =
1
1 mi 1.094 yd 1000 m
Do your units all cancel?
How many significant figures?
What is the correct answer?
Does this seem reasonable?
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Temperature Conversions
There are three scales used for measuring
temperature:
Fahrenheit – Part of the English System
Celsius – Used in the metric system
Kelvin – The base unit in the SI units and also
known as the absolute scale.
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Temperature Conversions
The thermometers
indicate the
freezing pts and
boiling pts on
each scale.
Notice there is an
equal distance
between the 2
pts on the Celsius
and Kelvin scales,
but not the
Fahrenheit.
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Temperature Conversions
There are simple equations you
can use to convert
temperatures from one scale
to another.
Celsius -> Kelvin
Because these units are equal,
all we have to do is add 273 to
the Celsius temperature.
T°C + 273 = TK
Kelvin -> Celsius
TK - 273 = T°C
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Temperature Conversions
When converting with the
Fahrenheit scale we
must do more math
because the scales are
not equal units.
Celsius ->Fahrenheit
T°F=1.80(T°C)+32
Fahrenheit -> Celsius
T°C= T°F – 32
1.80
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Temperature Conversions
Convert the following:
1. 145 °C = K
2. 373 K = °C
3. 25 °C = K
24
5.8 Density
Objective: To define density and its units.
Density: the amount of matter present in a given
volume of substance or is mass per unit volume.
In mathematical terms this means:
Density = mass
volume
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Density
What type of units would you use for density?
Mass => ? Units
Volume => ? Units
Mass = grams (g)
Volume = milliliters (ml) = cubic cm = cm3/cc
So density units = g/ml or g/cm3
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Density
So what does the term density really mean?
If something is very dense...what does that mean?
What if something is not very dense?
You know how to calculate density, but how would you
measure density?
What type of instruments would you need?
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