Transcript Si units - Neshaminy School District

Data Analysis
Si units
Metric System Review
SI units
 Used in nearly every country in the world,
the Metric System was devised by French
scientists in the late 18th century. The goal
of this effort was to produce a system that
used the decimal system rather than
fractions as well as a single unified system
that could be used throughout the entire
world.
 In 1960, an international committee of
scientists revised the metric system and
renamed it the Systeme International
d”Unites, which is abbreviated SI.
There are seven base units in SI. A base
unit is a defined unit in a system of
measurement that is based on an object or
event in the physical world.
 The REAL kilogram,
the International
Prototype Kilogram
(IPK) is kept in the
International Bureau
of Weights and
Measures near
Paris. Several official
clones of this
kilogram are kept in
various locations
around the globe.
 A subset of the prefixes is Tera- (12), Giga(9), Mega- (6), Micro- (-6), Nano- (-9), Pico(-12), Femto- (-15), Atto- (-18):
 The Gooey Monster May Not Pick Five
Apples.

Converting With SI (metric)
 When converting within the metric system it
is simply a measure of moving the decimal
in the appropriate direction.
Converting With SI (metric)
 Kangaroos Hop Down Mountains Drinking
Chocolate Milk
 Kilo Hecto Deca Meter Deci Centi Milli
 1000 100 10 1 .1 .01 .001
 1000 m = ______ km
 .001 hg = ______ dg
 42.7 L = _____ cL
Things to remember
1.
The short forms for metric units are called symbols, NOT
abbreviations
2.
Metric symbols never end with a period unless they are
the last word in a sentence.
•
•
3.
RIGHT: 20 mm, 10 kg
WRONG: 20 mm., 10 kg.
Metric symbols should be preceded by digits and a
space must separate the digits from the symbols
•
•
RIGHT: the box was 2 m wide
WRONG: the box was 2m wide
Things to remember
1.
The short forms for metric units are called symbols, NOT
abbreviations
2.
Metric symbols never end with a period unless they are
the last word in a sentence.
•
•
3.
RIGHT: 20 mm, 10 kg
WRONG: 20 mm., 10 kg.
Metric symbols should be preceded by digits and a
space must separate the digits from the symbols
•
•
RIGHT: the box was 2 m wide
WRONG: the box was 2m wide
Things to remember
4. Symbols are always written in the singular form
•
•
•
RIGHT: 500 hL, 43 kg
WRONG: 500 hLs, 43 kgs
BUT: It is correct to pluralize the written out metric
unit names: 500 hectoliters, 43 kilograms
5. The compound symbols must be written out with
the appropriate mathematical sign included
•
•
•
RIGHT: 30 km/h, 12 cm/s
WRONG: 30 kmph, 30 kph (do NOT use a p to
symbolize “per”)
BUT: It is ok to write out “kilometers per hour”
Things to remember
6. The meaning of a metric symbol is
different depending on if it is lowercase or
capitalized
•
•
mm is millimeters (1/1000 meters)
Mm is Megameters (1 million meters)
A unit that is defined by a combination of
base units is called a derived unit. The
derived unit for volume is the cubic
centimeter (cm3), which is used to
measure volume of solids, one cm3 is
equal to 1 ml. 1000 mL is equal to 1 Liter.
Quantity measured
Unit
Symbol
millimeter
mm
10 mm =
1 cm
centimeter
cm
100 cm =
1m
meter
m
kilometer
km
1 km =
milligram
mg
1000 mg =
gram
g
kilogram
kg
metric ton
t
Time
second
s
Temperature
degree Kelvin
K
square meter
m²
hectare
ha
square kilometer
km²
1 km² =
milliliter
mL
1000 mL =
cubic centimeter
cm³
1 cm³ =
1 mL
liter
L
1000 L =
1 m³
cubic meter
m³
Length, width,
distance, thickness,
girth, etc.
Mass
(“weight”)*
Area
Volume
Relationship
1 kg =
1t =
1 ha =
1000 m
1g
1000 g
1000 kg
10 000 m²
100 ha
1L
Another derived unit is Density is a ratio that
compares the mass of a unit to its volume.
The unit for density is g/ cm3 or kg/m3.
 Density = mass ÷ volume
 or
Density = Mass
Volume
 Temperature Conversions
 Temperature is defined as the average
kinetic energy of the particles in a sample of
matter. The units for this are oC and Kelvin
(K). Note that there is no degree symbol for
Kelvin.

 Heat is a measurement of the total kinetic
energy of the particles in a sample of matter.
The units for this are the calorie (cal) and
the Joule (J).
 The following equation can be used to convert
temperatures from Celsius
b (t) to Kelvin (T) scales:
 T(K) = t(oC) + 273.15
 You are simply adding 273.15 to your Celsius
temperature.
 Example: Convert 25.00 oC to the Kelvin scale.
 T(K) = 25.00 oC + 273.15
 = 298.15

 Subtracting 273.15 allows
conversion of a Kelvin
temperature to a
temperature on the Celsius
scale. The equation is:
 t(oC) = T(K) - 273.15
 You are simply subtracting
273.15 from your Kelvin
temperature.
 You are simply subtracting 273.15 from your
Kelvin temperature.
 Convert the following from the Celsius scale to the
Kelvin scale.
 1. –200 oC
2. –100 oC
3. –50 oC

4. 10 oC
 8. 100 oC


5. 50 oC
6. 37 oC
9. –300 oC
11. 273.15 oC
10. 300 oC
12. -273.15 oC
 Convert the following form the Kelvin scale
to the Celsius scale.
 1. 0 K
2. 100 K 3. 150 K
 4. 200 K
5. 273.15 K
 6. 300 K
7. 400 K 8. 37 K
 9. 450 K
10. –273.15 K
 Using your calculator to perform math
operations with scientific notation
 A calculator can make math operations with
scientific notation much easier.

Using your calculator to
perform math operations with
scientific notation
 A calculator can make math operations with
scientific notation much easier. To add
 6.02 x 10-2 and 3.01 x 10-3, simply type the
following:

 6.02 EXP +/- 2 + 3.01 EXP +/3
 The calculator should read 6.321 –02. This
means 6.321 x 10-2.
Using your calculator to perform math
operations with scientific notation

 Calculators vary. Instead of EXP, some
have EE. Instead of +/-, some have (-).
Only use the +/- or (-) if the exponent is
negative.
 It is also important to keep in mind that
when the EXP button is hit, it is as though
the button said “x 10 to the.” THERE IS NO
NEED TO PRESS THE MULTIPLICATION
BUTTON (unless the numbers in the
problem are being multiplied together).
 To multiply 6.02 x 10-2 and 3.01 x 10-3,
simply type the following:

 6.02 EXP +/- 2 x 3.01 EXP +/- 3
=
 The calculator should read 1.812 02 -04.
This means 1.812 02 x 10-4. If you are
unsure, consult your teacher or the owner’s
manual for the calculator.
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Practice Section
(3.37 x 104) + (2.29 x 105)
(9.8 x 107) + (3.2 x 105)
(8.6 x 104) – (7.6 x 103)
(2.238 6 x 109) – (3.335 7 x 107)
Multiplication and Division – Significant
digits should be used in your answers!!!!!!!
(1.2 x 103) x (3.3 x 105)
(7.73 x 102) x (3.4 x 10-3)
(9.9 x 106)  (3.3 x 103)
8. . (1.55 x 10-7)  (5.0 x 10-4)
Dimensional Analysis
 Dimensional analysis is the algebraic
process of changing from one system of
units to another. A fraction, called a
conversion factor, is used. These
fractions are obtained from an equivalence
between two units.
 http://www.youtube.com/watch?v=hQpQ0hx
VNTg&list=PL8dPuuaLjXtPHzzYuWy6fYEa
X9mQQ8oGr&index=2
1 in
2.54 cm
Dimensional Analysis
 For example, consider the equality 1 in. =
2.54 cm. This equality yields two
conversion factors which both equal one:
1 in
2.54 cm
Dimensional Analysis
Note that the conversion factors above both
equal one and that they are the inverse of one
another. This enables you to convert between
units in the equality. For example, to convert
5.08 cm to inches
 5.08 cm x = 2.00 in
Dimensional Analysis
For example, to convert 5.08 cm to inches
 5.08 cm x = 2.00 in
USING DIMENSIONAL
ANALYSIS
 You must develop the habit of including
units with all measurements in calculations.
Units are handled in calculations as any
algebraic symbol:
 Numbers added or subtracted must have
the same units.
Representing Data
Graphing
 Circle Graph (pie chart)
 Useful for showing parts of a fixed whole.
Dimensional Analysis
(Conversions)
 Units are multiplied as algebraic symbols.
For example: 10 cm x 10 cm = 10 cm2
 Units are cancelled in division if they are
identical.
 For example, 27 g ÷ 2.7 g/cm3 = 10 cm3.
Otherwise, they are left unchanged. For
example, 27 g/10. cm3 = 2.7 g/cm3.
Dimensional Analysis
(Conversions)
Dimensional Analysis
(Conversions)
 Now use dimensional analysis to solve the
following English to metric measurement
conversion problems:
 (Use the equivalencies in the box on the
previous page for your conversion factors).
 Remember to use units so that you can
cancel the ones you don’t want in your
answer and keep the ones that you do!
Dimensional Analysis
(Conversions)
 1. Convert 5.00 lb to g
(2270 g)


 2. Convert 8.00 in. to m
( 0.203 m)
Dimensional Analysis
(Conversions)
 Try the rest of these on your own using
dimensional analysis:
 Convert 3.00 lb to g

 How many m are in 9.00 in?
Accuracy and Precision
 Accuracy refers to how close a measured
value is to the accepted value.
 Precision refers to how close a series of
measurements are to one another.
Accuracy and Precision
 Accuracy refers to how close a measured
value is to the accepted value.
 Precision refers to how close a series of
measurements are to one another.
Accuracy and Precision
Percent Error
 Ratio of an error to an accepted value
 Percent Error is a way of expressing how
far off an experimental measurement is from
the accepted/true value. The formula for it
is:
 Percent Error is a way of expressing how
far off an experimental measurement is from
the accepted/true value. The formula for it
is:
 A 9th grade physical science student finds
the density of a piece of aluminum to be
2.54 g/cm3. The accepted value is 2.7
g/cm3. What is the percent error? Show
your work and make sure that you have the
correct number of significant digits.
 A student measures the length of a cube of
metal to be 2.12 cm. The actual length is
2.21 cm. What is the percent error? Show
your work and make sure that you have the
correct number of significant digits.
 A student performs an experiment and
calculates the strength of an acid as 0.015 8
M. The actual strength is 0.016 5 M . What
is the percent error? Show your work and
make sure that you have the correct number
of significant digits.
Representing Data
Graphing

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

Bar Graph
Useful for understanding trends.
Works well with data in catagories.
Often used to show how quantities vary with
factors such as time, location, and
temperature.
Representing Data
Graphing
 Bar Graph
 Independent variable plotted on the x-axis
 Dependent variable plotted on the y- axis
Representing Data
Graphing



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
Line Graphs (two coordinate graphs)
Most of the graphs used in chemistry
Plot points have an x and y coordinate
Independent variable plotted on the x-axis
Dependent variable plotted on the y- axis
Line Graphs
 Best fit line (trend line)
straight line drawn so as many points fall
above the line as below the line.
Line Graphs
 Slope
 Positive
slope shows a
direct
relationship
(e.g.as the
IV
increases
the DV also
Line Graphs
 Slope
 Positive
slope shows a
direct
relationship
(e.g.as the
IV
increases
the DV also
increases)
Line Graphs
 Slope
 Positive slope - shows a direct relationship
(e.g.as the IV increases the DV also
increases)
 Negative slope - shows a direct relationship
(e.g.as the IV increases the DV also
increases)
Significant Figures
(Sig Figs)
 Counting Significant Digits
 Quantities in chemistry are of two types:
 Exact numbers – These result from counting
objects such as desks (there are 24 desks in this
room), occur as defined values (there are 100 cm
in 1 m), or as numbers in formulas (area of a right
triangle = ½ B x H). They (24, 100, 1, and ½ for
these examples) all have an infinite(∞) number of
significant digits. B and H are measurements and
do not have an infinite number of digits.
 Inexact numbers – These are obtained
from measurements and require judgment.
Uncertainties exist in their values.
 When making any measurement, always
estimate one place past what is actually
known. For example, if a meter stick has
calibrations to the 0.1 cm, the
measurement must be estimated to the 0.01
cm. When making a measurement with a
digital readout, simply write down the
measurement. The last digit is the
estimated digit.
 Significant digits are all digits in a number
which are known with certainty plus one
uncertain digit. The following rules can be
used when determining the number of
significant digits in a number:
The following rules can be used when determining the number of
significant digits in a number:
EXAMPLE
1.
All nonzero numbers are significant.
132.54 g
SIG
FIGS
5
2.
All zeros between nonzero numbers
are significant.
130.0054 m
7
3.
Zeros to the right of a nonzero digit
but to the left of an understood
decimal point are not significant
unless shown by placing a decimal
point at the end of the number.
190 000 mL
2
190 000. mL
0.000 572 mg
6
3
460.000 dm
6
RULE
4.
All zeros to the right of a decimal
point but to the left of a nonzero digit
are NOT significant.
5.
All zeros to the right of a decimal
point and to the right of a nonzero
digit are significant.
 You can remember these rules or learn this
very easy shortcut.
 If the number contains a decimal point, draw
an arrow starting at the left through all zeros
and up to the 1st nonzero digit. The digits
remaining are significant.
 Try these:
 0.002 5
1.002 5
0.002 500 0
14 100.0
 If the quantity does not contain a decimal
point, draw an arrow starting at the right
through all zeroes up to the 1st nonzero
digit. The digits remaining are significant.
 Try these:
 225
10 004
14
100
103
 A good way to remember which side to start
on is:
 decimal point present, start at the Pacific
 decimal point absent, start at the Atlantic
Practice Section - How many significant digits do
each of the following numbers have?
Practice Section - How many significant digits do each of the following numbers
have?
1.
2.
3.
4.
5.
1.050 _____ 6.
20.06 _____ 7.
13
_____ 8.
0.303 0 ____ 9.
373.109 ____10.
420 000 ______
970
______
0.002 ______
0.007 80 _____
145.55 _____
Homework Section
How many significant digits do the
following numbers possess?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
0.02
0.020
501
501.0
5 000
5 000.
6 051.00
0.000 5
0.102 0
10 001
11. 20.03 kg
12. The 60 in the equality
60 s equals one min.
13. The one in the above.
14. 120 m
15. 10 dollar bills
16. 0.050 cL
17. The ½ in ½ mv2
18. 0.000 67 cm3
Rounding Rules
 Calculators often give answers with too
many significant digits. It is often necessary
to round off the answers to the correct
number of significant digits. The last
significant digit that you want to retain
should be rounded up if the digit
immediately to the right of it is
 (Each of the examples are being rounded to
four sig digs):
Rounding Rules
The last significant digit that you want
to retain should be rounded up if the
digit immediately to the right of it is
Rule
Example
4 sig digs
….. greater than 5
532.79
532.8
….. 5, followed by a nonzero digit
17.255 1
17.26
….. 5, not followed by a nonzero, but has an 3 213.5
odd digit directly in front of it.
3214
Rounding Rules
 The last significant digit that you want to retain
should stay the same if the digit immediately
to the right of it is:
Rule
Example 4 sig
digs
….. less than 5
5454.33
5454
….. 5, not followed by a nonzero, but has
an even digit directly in front of it.
0.00785
0.0078
Rounding Rules
 Practice Section - Round the following numbers to 3 sig digs.
 1. 279.3 _________ 4. 32.395 ________ 7. 18.29 ___________
 2. 42.353 ________ 5. 32.25 ________ 8. 5 001
___________
 3. 18.77 _________ 6. 7.535 _______ 9. 0.008 752 __________
Rounding Rules
 Homework Section - Round the following numbers to 4
significant digits
 123 456
 0.093 459
 1.234 567 890
 222.251
 222.26
 222.24
 222.25
 222.35
 5 000
 19.999
Line Graphs
 Slope
 Use data points
to calculate the
slope of the
line.
 The slope is the
change in y
divided by the
change in y.