Transcript Measuring

Scientific Notation
• Scientific notation expresses numbers as a
multiple of two factors: a number between 1
and10; and ten raised to a power, or
exponent.
6.02 X 1023
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Scientific Notation
• When numbers larger than 1 are expressed in
scientific notation, the power of ten is
positive.
2500 = 2.5 X 103
• When numbers smaller than 1 are expressed
in scientific notation, the power of ten is
negative.
.0025 = 2.5 X 10-3
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Convert Data into Scientific Notation
• Change the following data into scientific
notation.
A. The diameter of the Sun is 1 392 000 km.
B. The density of the Sun’s lower atmosphere
is 0.000 000 028 g/cm3.
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Convert Data into Scientific Notation
• Move the decimal point to produce a factor
between 1 and 10. Count the number of
places the decimal point moved and the
direction.
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Convert Data into Scientific Notation
• Remove the extra zeros at the end or
beginning of the factor.
• Remember to add units to the answers.
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MEASUREMENT
Measuring
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The numbers are only half of a measurement.
It is 3 long.
3 what.
Numbers without units are meaningless.
How many feet in a yard?
3 ft
You always need a numerical and unit value!
• In 1795, French scientists adopted a
system of standard units called the
metric system.
• In 1960, an international committee of
scientists met to update the metric system.
• The revised system is called the Système
Internationale d’Unités, which is
abbreviated SI.
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Units of Measurement
• Throughout any natural science course we are going to deal
with numbers. Numbers by themselves are meaningless. That
is why need to have some sort of reference or standard to
compare to. International System of Units or SI units, is based
on the metric system.
Quantity
Base Unit
Symbol
Length
Meter
m
Mass
Gram (Kilogram)
g (kg)
Time
Second
s
Temperature
Kelvin
k
Amount of
substance
Mole
mol
Electric current
ampere
A
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Prefixes of the SI Units
• Since the SI Units are based upon the metric system, we use
prefixes to change the quantity we are discussing about which
use multiples of ten.
• Some standard prefixes are:
Prefix
Abbreviation
Meaning
Mega-
M
106
Kilo-
k
103
Deci-
d
10-1
Centi-
c
10-2
Milli-
m
10-3
Micro-
µ
10-6
Nano-
n
10-9
Pico-
p
10-12
Examples:
1 megabyte =
1,000,000 bytes
1 microgram =
0.000001 grams
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The Metric System
An easy way to measure
The Metric System
- Decimal system
- Powers of 10
- 2 Parts :
Prefix – how many multiples of 10
milli, centi, Mega, micro
Base Unit - meter, liter, gram……
ex. Millimeter, centigram, kiloliter
Base Units
Length
- meter
(m)
Mass
- gram
(g)
Time
- second
(s)
Temperature
- Kelvin or ºCelsius ( K or C )
Energy
- Joules
(J)
Volume
- Liter
(L)
Amount of substance - mole
( mol )
Prefixes
Giga
1 000 000 000
G
109
Mega
1 000 000
M
106
kilo
1 000
k
1000 = 103
hecto
1 00
h
100 = 102
deka
10
da
10 =
base
1
g, L, sec, m, etc.
1 = 100
deci
1/10
d
.1 =
centi
1/100
c
.01 = 10-2
milli
1/1 000
m
.001 = 10-3
micro
nano
pico
1/1 000 000
μ
10-6
1/1 000 000 000
n
10-9
1/1 000 000 000 000
p
10-12
101
10-1
Converting
• how far you have to move on a chart, tells you
how far, and which direction to move the decimal
place.
• You need the base unit :
• You need a chart!
• You need a plan!
(meters, Liters, grams,)
etc.
Dr – uL Rule
Down right
up Left
21.5 g = __________mg
21,500
345.6 m = ___________
0.3456
km
Giga
1 000 000 000
G
109
Mega
1 000 000
M
106
kilo
1 000
k
1000 = 103
hecto
1 00
h
100 = 102
deka
10
da
10 =
BASE
1
g, L, sec, m, etc.
deci
1/10
d
.1 =
centi
1/100
c
.01 = 10-2
milli
1/1 000
m
.001 = 10-3
micro
nano
pico
1/1 000 000
μ
10-6
1/1 000 000 000
n
10-9
1/1 000 000 000 000
p
10-12
101
1 = 100
10-1
Conversions
k h D
d c m
• Change 5.6 m to millimeters
starts at the base unit and move three to
the right.
move the decimal point three to the right
56 00
Conversions
k h D
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d c m
convert 25 mg to grams
convert 0.45 km to mm
convert 35 mL to liters
It works because the math works, we are dividing
or multiplying by 10 the correct number of times
Accuracy and Precision
• When scientists make measurements, they
evaluate both the accuracy and the precision
of the measurements.
• Accuracy refers to how close a measured
value is to an accepted value.
• Precision refers to how close a series of
measurements are to one another.
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Accuracy and Precision
• Precision
– A measurement of how well
several determinations of the
quantity agree.
• Accuracy
– The agreement of a measurement
with the accepted value of the
quantity.
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Accuracy and Precision
• An archery target illustrates the difference
between accuracy and precision.
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SIGNIFICANT FIGURES
Significant Figures
Let’s take a look at some instruments used to
measure
--Remember: the instrument limits how good
your measurement is!!
Uncertainty in
Measurements
Different measuring devices have different uses
and different degrees of accuracy.
Significant figures (sig figs)
• We can only MEASURE at the lines on the
measuring instrument
• We can (and do) always estimate between the
smallest marks.
1
2
3
4
5
in
4.5 inches
What was actually measured?
4 inches
What was estimated?
0.5 inches
1
2
3
4
5
in
Significant figures (sig figs)
• The better marks… the better we can measure.
• Also, the closer we can estimate
1
2
3
4
5
ii
nn
4.55 inches
What was actually measured?
4.5 inches
What was estimated?
0.05 inches
1
2
3
4
5
i
n
So what does this all mean to you?
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Whenever you make a measurement, you
should be doing three things……
1. Check to see what the smallest lines
(increments) on the instrument represent
2. Measure as much as you can (to the smallest
increment allowed by the device)
3. Estimate one decimal place further than you
measured
Decimal Places Review
23456.789
ten thousands
thousands hundreds
tens
ones
thousandths
tenths hundredths
Your estimate MUST always be one (and
only one) decimal place further to the
right than your measurement
Practice
Your graduated cylinder can only accurately
measure to tens of mL. To what decimal
place should you estimate?
A balance can accurately measure to
hundredths of grams. What decimal place
will your estimate be?
Work Backwards Now
Look at the following measurements and determine
the smallest increment that the measuring
instrument could accurately measure to. Keep in
mind that the last significant figure is the estimate.
ones
100.3 g
tens
207 L
thousands
1500 cm
One-hundred thousandths
0.0004467 kg
What is measured and what is estimated in the
following measurements?
(Remember, significant figures include measured & estimated digits )
100.3
4 Sig Figs ; Measured: 100. ; Estimated: 0.3
207
3 Sig Figs ; Measured: 2.0 X 102 ; Estimated: 7
1500
2 Sig Figs ; Measured: 1000 ; Estimated: 500
0.0004467
4 Sig Figs ; Measured: 0.000446; Est: 0.0000007
SIGNIFICANT FIGURES
The RULES
Significant Figures
• The term significant figures refers to digits
that were measured.
• When rounding calculated numbers, we pay
attention to significant figures so we do not
overstate the accuracy of our answers.
Significant Figures
1. All nonzero digits are significant.
2. Zeroes between two significant figures are
themselves significant.
3. Zeroes at the beginning of a number are
never significant.
4. Zeroes at the end of a number are
significant if a decimal point is written in
the number.
Significant Figures
What about the Zeros??
B
M
E
Beginning
Middle
End
N
A
P
Never
Always
Point
Significant Figures in
Calculations
• When addition or subtraction is performed,
answers are rounded to the least significant
decimal place.
• When multiplication or division is
performed, answers are rounded to the
number of digits that corresponds to the
least number of significant figures in any of
the numbers used in the calculation.
Sig figs.
• How many sig figs in the following
measurements?
• 458 g
• 4085 g
• 4850 g
• 0.0485 g
• 0.004085 g
• 40.004085 g
Sig. Fig. Calculations
Multiplication/Division
• Rules:
• The measurement w/ the smallest # of sig. figs
determines the # of sig. figs in answer
• Let’s Practice!!!
• 6.221cm x 5.2cm = 32.3492 cm2
4
2
 How many sig figs in final answer???
 And the answer is….
32 cm2
For example
27.93 + 6.4 =

First line up the decimal places
27.93
+ 6.4
34.33
Then do the adding
Find the estimated numbers
in the problem
This answer must be rounded
to the tenths place = 34.3
Practice
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4.8 + 6.8765=
520 + 94.98=
0.0045 + 2.113=
6.0 x 102 - 3.8 x 103 =
5.4 - 3.28=
6.7 - .542=
500 -126=
6.0 x 10-2 - 3.8 x 10-3=
Dimensional Analysis
• The “Factor-Label” Method
– Units, or “labels” are canceled, or “factored” out
g
cm 

g
3
cm
3
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Dimensional Analysis
• Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each
bottom number.
4. Check units & answer.
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Dimensional Analysis
• Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
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Dimensional Analysis
• How many milliliters are in 1.00 quart of
milk?
qt
mL
1.00 qt
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
1L
1000 mL
1.057 qt
1L
= 946 mL
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Dimensional Analysis
lb
• You have 1.5 pounds of gold. Find its
volume in cm3 if the density of gold is 19.3
g/cm3.
cm3
1.5 lb 1 kg
2.2 lb
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1000 g
1 cm3
1 kg
19.3 g
= 35 cm3
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Dimensional Analysis
• How many liters of water would fill a
container that measures 75.0 in3?
in3
L
75.0 in3 (2.54 cm)3
(1 in)3
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1L
1000 cm3
= 1.23 L
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Dimensional Analysis
cm
Your European hairdresser wants to cut
your hair 8.0 cm shorter. How many
inches will he be cutting off?
8.0 cm
1 in
2.54 cm
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in
= 3.2 in
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Dimensional Analysis
Taft football needs 550 cm for a 1st down.
How many yards is this?
cm
yd
550 cm
1 in
1 ft 1 yd
2.54 cm 12 in 3 ft
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= 6.0 yd
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Dimensional Analysis
A piece of wire is 1.3 m long. How many
1.5-cm pieces can be cut from this wire?
cm
pieces
1.3 m
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100 cm
1 piece
1m
1.5 cm
= 86 pieces
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Density
• Density is a ratio that compares the mass of
an object to its volume.
• The units for density are often grams per
cubic centimeter (g/cm3 or g/mL).
• You can calculate density using this
equation:
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Density
• If a sample of aluminum has a mass of 13.5 g
and a volume of 5.0 cm3, what is its density?
• Insert the known quantities for mass and
volume into the density equation.
• Density is a property that can be used to
identify an unknown sample of matter. Every
sample of pure aluminum has the same density.
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% Error
% error = O - A
A
X 100
O = experimental value obtained (observed)
A = actual value (what you should get: text book)
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% Error
1.) What is the percent error in a lab if you find
the reaction produces12.052 grams of
calcium oxide. The text shows this reaction
should produce 13.512 grams.
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FINALLY!!!!!