# Scientific Notation

```Scientific Notation
Scientific Notation
 Very large or small numbers can be written in scientific
notation.
 Scientific notation uses decimals and a power of 10 to
represent the original number.
 To write a number is scientific notation, the number must be
written with a decimal point after the first digit.
Converting to Scientific Notation
Write out the entire number.
2. Count the number of places you move the decimal point so
that the number is after the first digit.
3. If you moved the decimal to the LEFT, write 10 raised to
the positive of the number of places you moved the
decimal.
4. If you moved the decimal to the RIGHT, write 10 raised to
the negative of the number of places you moved the
decimal.
1.
Write In Scientific Notation
1025000
0.00257
9810000
0.2365
Measuring Accurately
Accuracy vs. Precision
Accuracy
 The extent to which a
measured value agrees
with the accepted value
 Percent error between
experimental or
calculated numbers and
accepted number
Precision
 Degree of exactness to
which a quantity is
measured.
 Measurements may be
precise, but may not be
accurate.
 Based on the scale of
the measuring devise.
Recording and Reporting
Measurements
 When recording a measurement, always record all values
given by the devise and the “guess” at the last place value.
 For example, if you measure a strip of paper to be 5.6 cm,
you would want to add one more digit to the end of your
number based on where you think the paper ends. If it ends
right on the 0.6 mark, then your value would be 5.60 cm. If
it appears to go halfway between 0.6 and 0.7 your value
would be 5.65 cm.
Liquid Measurements- Meniscus
• Water is a “sticky”
molecule.
• Water will climb the
sides of the glass.
• This is called the
Meniscus.
The Metric System
Space Station Issues
 The International Space Station (ISS) is regularly populated
with Russians, Americans, Japanese, and Europeans.
 Language is a problem.
 So math is not a problem, one system of units has been
Measure out
5
feet.
How many
meters is that?
The Metric System
 Mass (how heavy things are) is measured in
grams.
 Volume (how much space something takes
up) is measured in liters.
 Length (how far, long, wide something is)
is measured in meters.
Examples of Mass
A Penny weighs 2.5
grams
1 gram of pure gold is worth
~\$100
Examples of Volume
A Bottle of Soda
2 Liters
Gallon of Milk
3.8 Liters
http://www.doobybrain.com/2008/07/24/new-coca-cola-2-liter-contour-bottle/
http://www.citysackers.com/product_info.php?products_id=370
Examples of Length
A stride is approximately
meter
1
A car is approximately
4 meter
Importance of Prefixes
Which is easier to report?
.000000003 grams
or
3 nanograms
Prefixes
King Henry Died from drinking chocolate milk
Kilo =
1000
100
Deca = 10
Hecto =
Free = grams, liters, meters
.1
Centi = .01
Milli = .001
Deci =
http://www.fanpop.com/spots/chocolate-milk/images/1297950/title/choco-milk-photo
OR….
King Have Diamonds but diamonds cost money
Kilo =
1000
100
Deca = 10
Hecto =
Base unit= grams, liters, meters
.1
Centi = .01
Milli = .001
Deci =
http://www.fanpop.com/spots/chocolate-milk/images/1297950/title/choco-milk-photo
Convert
5000 grams to kilograms
K H D f d c m
5000.g
Convert
5000 millimeters to meters
Convert
15 deciliters to hectoliters
Practice Conversions
9000 mL to DL
.006 Km to m
54 cg to g
.408 L to dL
905 Hm to cm
9 g to Kg
Importance of the Metric System
Chemists work across the
globe to further our
understanding.
We need to be able to share
our information so that we
can make discoveries more
quickly.
Conversions
Conversions Simplify Life
Conversions allow you to
represent the same amount
in different units.
http://www.fiftybucksaweek.com/tag/eggs/
Consider Eggs
Eggs are not sold
eggs or 1 dozen.
1dozen = 12 eggs.
http://www.reuters.com/article/idUSTRE67J34H20100820
Units
Setting Up A
Converson…
Make sure you
have the same
units on the
top and the
same units on
the bottom
1 dozen = 3x dozen
__________
__________
12 eggs
36 eggs
1 dozen = 2x dozen
_________
12 eggs
____________
24 eggs
1 dozen = x? dozen
_________
12 eggs
__________
15 eggs
1 dozen = x dozen
___________
12 eggs
_____________
15 eggs
Step One: Cross Multiply
Step Two: Divide
Step Three: Check Units
1 dozen = x dozen
_____________
________________
12 eggs
30 eggs
=
=x
Pressure Conversions
1 atm = 760 Torr
4 atm = ???
1 atm
4 atm
=
760 Torr X Torr
In chemistry we don’t
use dozens. We use Moles.
A mole is a number of particles.
Number of Particles
23
10
1 Mole = 6.02 x
Particles
60,200,000,000,000,0
00,000,000,000
Particles
Mole Conversions
 One mole of an element has a specific mass.
 We can convert between moles and grams.
1 mole of Carbon = 12 grams
1 mole of Carbon = 12 grams
How many moles is 30
grams of Carbon?
1 mole of Oxygen = 32 grams
How many moles is 59
grams of Oxygen?
Math Review
You have 20 beads; 6 of them are red.
What is the percentage of red beads?
How much is 13% of 54?
How much is 54% of 120?
How much is 98% of 6?
35 = 70
5 + 6 = 26
50 =  + 70
5 − 10 = 10
25 =
75

3
14 =
2
2
= 64
2
+ 3 = 39
5  − 2 = 10
25
+ 50 = 55

+ 3=5
60
1 mole = 40 grams. How many moles
is 60 grams?
1 mole = 22.4 liters. How many liters
is 3 moles?
12 Eggs = 1 dozen eggs. How many
eggs is 4.66 dozen?
100 cents = 1 dollar. How many
dollars is 14,000 cents?
1 mole = 32 grams. How many grams
does 2.5 moles weigh?
1 atm = 760 Torr. How many Torr is
3.4 atms?
Significant Figures
Significant Figures
 When using a measuring device, the last digit is always an
estimate.
 To make sure all calculations with measurements are
accurate, we have to make sure our answers do not have
more digits than the original measurements.
 Scientists use significant figures to help solve this issue.
 The more sig figs a measurement has the more precise it is.
What Numbers are Significant?
 All digits other than zero are significant numbers.
 Zeros are significant if:
 It is surrounded by two non-zero digits
 If more than one zero is surrounded by non-zero numbers, all
the surrounded zeros are significant
 If a decimal is present, all the zeros after the first non-zero
number are significant
 All numbers written in scientific notation are significant
Steps to Counting Sig Figs
Step 1: Is the decimal point present or absent?
Present: start from left
Absent: start from right
Step 2: Start counting with the first number that isn’t zero
Step 3: Once you start counting, count everything, including
zeros
The Rules of Zero
How many significant figures?
Pacific
Present
Left
0.554
Atlantic
Absent
Right
3 Sig Figs
The Rules of Zero
How many significant figures?
Pacific
Present
Left
8004
Atlantic
Absent
Right
4 Sig Figs
The Rules of Zero
How many significant figures?
Pacific
Present
Left
1.0450
Atlantic
Absent
Right
5 Sig Figs
The Rules of Zero
How many significant figures?
Pacific
Present
Left
60650
Atlantic
Absent
Right
4 Sig Figs
The Rules of Zero
How many significant figures?
Pacific
Present
Left
900.0
Atlantic
Absent
Right
4 Sig Figs
The Rules of Zero
How many significant figures?
Pacific
Present
Left
733
Atlantic
Absent
Right
3 Sig Figs
Identify the number of
significant figures:
 1.03690
 100000
 900.0
 0.000002369
 0.00450
 10679.0
Do Now:
 Solve for x: x2 – 5 = 29
 How many significant figures: 0.00150
 18% of 105 is how much?
 What units would you measure the volume of a pool in?
 Convert from scientific notation: 2.3 x 10-4
Calculations with Sig Figs
 When you multiply or divide the answer must have has many
sig figs as the least precise number.
 When you add or subtract the answer must have the same
number of digits after the decimal place as the number with
the fewest digits after the decimal place.
Perform each operation:
 103 x 2.0
 684.9 x 42.3
 300 / 50.00
 2369 / 3
 462.7 + 82.697
 945.0526 + 1
 695.336 – 452.2214
 6547.9999 – 4521.0
Graphing
Graphing
 Remember to SLAP IT
 Scale- does your scale cover all data?
 Label- did you label each axis with units?
 Axis- is your independent variable on the x-axis and your
dependent variable on the y-axis?
 Plot Points- are all points properly plotted?
 Investigate- have you looked for trends and relationships
between the variables graphed?
 Title!- does your graph have an appropriate title?
Reference Table Graphs
 There are two graphs you need to be familiar with in your




reference table.
They are in Table G: Solubility Curves at Standard Pressure
and Table H: Vapor Pressure of Four Liquids.
To be able to read these graphs, you need to first identify
which graph will give you the information you need. The
title and axis labels will tell if the graph has the information
you need.
Now you need to identify the scale used on each axis.
Once these steps are done, use the given information in the
problem to determine your missing information.
Example
 What is the solubility of NH3 at 55C?
 At which temperature does NaNO3 have a solubility of 100 g
solute/100g H20?
 Which liquid has a vapor pressure of 150 kPa at 90 C?
 At what temperature does water have a water vapor of
101.3kPa?
Using Graphs
 One important piece of information you can use from a
linear graph is the slope.
 To find slope, use the formula:
Slope = y2 – y1
x2 – x1
Example:
Find the slope of this graph:
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