Transcript Using Scientific Measurments

USING SCIENTIFIC MEASUREMENTS
SIGNIFICANT FIGURES

Significant Figures: Consist of all the digits known
with certainty plus one final digit (This digit is
estimated by you)
The larger
markings are
labeled every 10
milliliters (mL).
In between the
larger labeled
markings are
short marks
every 1 mL. The
reading for this
would be
35.0mL with the
.0 being the
uncertain #.
6.30 cm
6.35 cm
6.40 cm
READING MEASUREMENTS FOR SIG FIGS
•When reading an Electric Scale there is no need to
add on a number. All numbers available are to be
used and considered significant.
RULES FOR DETERMINING SIG FIGS
 1) ALL numbers that aren’t zero (1,2,3,4,5,6,7,8,9) are




significant. Ex-83765 (5)
2) ALL zeroes between non-zero numbers are
significant. Ex- 404 (3)
3) ALL zeroes which are at the end of a number and to
the right of the decimal point are significant.
Ex-1.5600 (5)
4) Zeros appearing in front of all non-zero digits are
NOT significant. Ex-0.0012 (2) 10.0090 (6)
5)Zeros at the end of a number but to the left of a
decimal point are significant only if a decimal point has
been placed to the right of that zero. If there is no
decimal point then they are NOT significant.
Ex-5000 (1) 5000. (4) 750 (2)
ROUNDING RULES
Find the number you want to keep
and look at the next number:
If it is…..
Examples:(rounded
to 3 sig figs)
Greater than 5, increase the last digit by 1.
Less than 5, do not change the last digit.
56.87g …..56.9g
12.02 L ….12.0 L
Equal to 5, followed by a number other than
zero, increase the last digit by 1.
3.7851 s …. 3.79s
Equal to 5, followed by nothing or a zero
If the number you are keeping is odd,
increase the odd digit by 1.
2.835 m ….2.84 m
(because 3 is odd)
Equal to 5, followed by nothing or a zero
If the number you are keeping is even, do
not change the even digit.
2.645 mL …. 2.64 mL
(because 4 is even)
SIG FIG PRACTICE









Determine the number of Sig Figs
4932.20 cm
0.0400 L
804.5 g
0.0144030 km
1002 m
400 mL
30000. cm
0.0000625000 kg
Suppose the value “seven thousand cm” is reported to
you. How would it be expressed if:
You wanted to indicate1 Sig Fig
 You wanted to indicate 4 Sig Figs
 You wanted to indicate 6 Sig Figs

SIGNIFICANT FIGURES
Addition and Subtraction Rules
 The answer must be rounded so that it contains the
same number of digits to the right of the decimal point
as there are in the measurement with the smallest
number of digits to the right of the decimal point.

Ex. 2.89 m + 0.00043 m = 2.89043 m = 2.89 m
Multiplication Rules
 The product or quotient should be rounded off to the
same number of significant figures as in the
measurement with the fewest significant figures.


Ex. 3.5293 mol x 34.2 g/mol = 120.70206 g = 121 g
Conversion Factors and Sig Figs: Conversion
Factors do not affect the amount of Sig Figs because
they are exact. This means there is no error in them.
 Scientific
Notation: A method of writing very large
and very small quantities as a number times 10 to
a power : M x 10n (Example-1404 = 1.404 x 103)
 Keep all sig figs unless told otherwise.
SCIENTIFIC NOTATION
1.
2.
3.
4.
5.
Find the decimal
569000.00
Move (or jump) the decimal until you have one digit to the
left of the decimal 569000.00
Count the # of jumps (jumped left # is pos, jumped right #
is neg) pos neg
569000.00
Rewrite the number with the decimal in the new place and
attach x 10
5.69 x 10
Add the number of jumps as an exponent on the x 10
5.69 x 105
 Quantity-Anything
that is measurable (has magnitude,
size, or amount) ex- length, time, volume, mass…..etc.
 Measurement-Represents a quantity with a # and unit
 SI Base Units: The International System of Units
1-Length- l
meter-m
3-Time- t
seconds-s
2-Mass- m
kilogram-kg
4-Temperature- T
Kelvin-K
5-Amount of Substance-n
mole-mol
CONVERTING TEMPERATURE
Ko= Co + 273.15
Fo = 9/5 (Co+32)
Co = 5/9(Fo-32)
Convert the following to Kelvin
1) 0o C ________
2) -50o C ________
3) 90o C ________
4) -20o C ________
Convert the following to Celsius
5) 100o K
6) 200o K
7) 273o K
8) 350o K
________
________
________
________
UNITS CONTINUED
 Derived
Units: Any combination of SI Base Units
 Density:
g/cm3

Weight-Measure of the gravitational pull on matter
(measured with a Spring Scale)

Newtons=kg • m
s2
MASS (m)
Mass is the amount of matter present. How much
stuff is there?
 Mass and weight are not the same thing
 Why do they seem the same here on earth?
 Will a person’s mass change on the moon?
 Will a person’s weight change on the moon?

VOLUME (V)
Volume is a measure of how much space an object
takes up.
 Measure volume in 2 ways


Solid straight sided objects-metric: cm3, m3, mm3, etc


Liquids and odd shaped objects: mL, L, kL, cL, etc


LxWxH=Volume
Use Graduated Cylinder or use water displacement
1mL=1cm3
 Density:
The ratio of mass to volume
 D=m/V
 All substances have a very specific
density.
 Density graphs are Directly Proportional
 What would have to change to make
density vary?
Density=
19.32 g/cm3
Density=
19.32 g/cm3
Gold
Memorize: Water has a density of 1g/mL or 1g/cm3
Density Column
1-Which Sample would
be at the top of the
column?
2-Which sample would
fall to the bottom of the
column?
DENSITY PRACTICE PROBLEMS

Silver has a density of 10.5 grams/cm3 and gold
has a density of 19.3 g/cm3. Which would have
the greater mass, 5cm3 of silver or 5cm3 of gold?


Gold with 96.5 g
An irregularly shaped stone was lowered into a
graduated cylinder holding a volume of water
equal to 2 ml. The height of the water rose to 7
ml. If the mass of the stone was 25 g, what was
its density?

Density=5 g/mL
ACCURACY AND PRECISION

Accuracy-The closeness of measurements to the
correct or accepted value
 How

close was your measured value to the accepted value?
Precision-The closeness of a set of measurements
of the same quantity made in the same way.

How reproducible are your measurements?
% ERROR

% Error: This is used to find out how accurate a
measurement or average measurement is.



(Subtract the accepted value from the measured
value, divide by the accepted value) multiply by 100
measured-accepted x 100 = % Error
accepted
Negative sign (-) means measured # was smaller
Positive sign (+) means measured # was bigger
Ex. If the accepted Density of cork is .24 g/cm3
and you measured it to be .26 g/cm3 then the %
error would be:
.26 g/cm3 - .24 g/cm3 x 100 = 8.3%
.24 g/cm3

CONVERTING BETWEEN UNITS
Dimensional Analysis: An equation used to solve a problem
using units or labels. Also called the factor label method.
 It is used to go from one unit to another.
 Conversion Factor: Relationship between the two units.


You must ask how much of one does it takes to equal the other?
Conversion
Factor
Equation:
Starting Amount

= Finishing Amount
Example of conversion factor for dollars and quarters
4 quarters
1 dollar

finishing unit
starting unit
or
1 dollar
4 quarters
Example of conversion factor for cm and m
100cm
1m
or
1m
100cm
DIMENSIONAL ANALYSIS
Draw a T bar (Magic Bridge)
2. Find out the starting amount and unit. Hint**It’s a number
with a unit. Write it down in the upper left hand corner.
3. Now decide on the finishing unit.
4. Make 2 fractions out of the starting and finishing units.
How much of one equals the other?
5. Pick the fraction that has the starting unit on the bottom
and place it into your T bar on the right hand side.
6. Cancel out any units that will cancel.
7. Multiply the stuff on top and divide by the stuff on the
bottom.
1x10-9 1x10-6 .001
.01
.1
1
10
100 1000 1x106 1x109
G
M
k
h
da
m
d
c
m
µ
n
L
g
1.
PRACTICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
304.90 dimes  nickels
293 50 pennies  quarters
654 cm3  mL
8.90258 x104 Fingers  hands
6.29 x 1010 sec hours
5.43 x103 hr  weeks
45.5 cm  m
1.540 kg  µg
12.4 dL  hL
4.5 x 10-6 m  dm
9.21 kg  mg
.054 x103 Mm  nm
1x10-9
G
1x10-6 .001
M
k
.01
h
.1
da
1
m
L
g
10
d
100
c
1000 1x106 1x109
m
µ
n
CONVERTING VOLUME AND AREA
If you have a measurement that has a unit with an
exponent: for example: m2, cm3
 You must use the same number of conversion factors
as there is in the exponent.

Example: for m2 you would need to list the conversion
factor twice
 Example: for cm3 you would need to list the conversion
factor three times

CONVERTING UNITS OF VOLUME
1.
2.
3.
4.
5.
6.
7.
310 000 cm3 of concrete in cubic meters
6.5 m2 of steel sheet in square centimeters
0.035 m3 of chlorine gas in cubic centimeters
0.49 cm2 of copper in square millimeters
1200 µm2 of acetic acid solution in square decimeters
87.5 mm3 of actinium in cubic centimeters
250 000 cm2 of polyethylene sheet in hm2
EXAMPLES
1.
2.
3.
4.
5.
Your Eupopean Hairdresser wants to cut your hair
8.0 cm shorter. How many inches will he be cutting
off? (2.54cm = 1in)
The SGC Football team needs another 550cm for a
1st down. How many yards is this?
If Jules Vern expressed the title of his famous
book, “Twenty Thousand Leagues Under the Sea”
in feet, what would the title be?
(1mile = 5280ft, 1 League = 3.450miles)
A piece of wire is 1.4 m long. How many 1.5 cm
pieces can be cut from this wire?
You need a room that is at least 1.350 x 10-3 km2
for the Junior/Senior Prom. Your Cafetorium is
133.9ft wide and 67.02 ft long. Is the Cafetorium
big enough?