Transcript 10 x 10 x 10 x 10 - Hauppauge School District

Aim 1 – Chemistry Metrics
Question: How is the metric system used
in chem?
• Chemistry is:
– the branch of science
that deals with the
_________________
__________ of which
matter is composed;
– the investigation of
their properties and
the ways in which
they _____________
_________________
_________________
– and the use of these
processes to ______
_________________.
Chemistry and the Metric System
• The metric system is based on units of 10
• What is the English system (inches, feet,
pounds) based on?
• The metric system is used by virtually all
_________________________
Quantity
Base Unit
Length
Meter (m)
Mass
gram (g)
Volume
Liter (L)
Other units used
millimeter, centimeter,
kilometer
milligram, centigram,
kilogram
milliliter
Chemistry and the Metric System
• Length
– the measure of distance between two points
– _______________________
• Mass (def) - a measure of the ______________
in an object in grams
– 1 ounce = 28.3 g and ___________________
• Mass is different from:
– Weight (def) - the ______________________
upon an object – measured in pounds
– Volume (def) - the ___________________ an
object takes up – measured in L or mL
Converting metric units using prefixes
• Why there are metric prefixes?
– Measuring the volume of children’s Tylenol
is easier in __________________
__________________
– Measuring the distance from NY to LA is
more realistic in ____________________
– The dosage of acetaminophen in an
aspirin tablet is easier to measure in
_________________________________
• Prefixes simply change the size of the unit
by increasing or decreasing the value by a
__________________________________
Converting metric units using prefixes
The prefixes you must memorize are as follows:
• kilo
= 1000x the base unit
• hecto = 100x the base unit
• deka = 10x the base unit
• base = grams, meters, liters, seconds, etc
• deci
= 1/10x the base unit
• centi
= 1/100x the base unit
• milli
= 1/1000x the base unit
• micro = 1/1,000,000x the base unit
• pico
= 1/1,000,000,000x the base unit
Converting metric units using prefixes
• Each prefix moves the decimal by a factor
of 10
• MOVING DOWN the scale moves the decimal
place to the _______________________ by 10
• MOVING UP the scale moves the decimal
place to the _______________________ by 10
1 kilo = 10 hecto = 100 deka = 1,000 base units
1 base unit = 10 deci = 100 centi = 1,000 milli
1 base unit = 1,000,000 (1 million) micro
1 base unit = 1,000,000,000 (1 billion) pico
Converting
metric units
using
prefixes
The prefixes you
must memorize
are as follows:
kilo
= 1000x
hecto = 100x
deka = 10x
deci = 1/10x
centi = 1/100x
milli = 1/1000x
Example: Convert 124
milligrams to grams.
1. What is the conversion factor?
2. What does the proportion look
like for the conversion?
3. Solve for X:
Converting
metric units
using
prefixes
Example: Convert .003
kilometers to meters.
1. What is the conversion factor?
The prefixes you 2. What does the proportion look
like for the conversion?
must memorize
are as follows:
kilo
= 1000x
hecto = 100x
deka = 10x
3. Solve for X:
deci = 1/10x
centi = 1/100x
milli = 1/1000x
1. Convert 1.2 kilometers to
Practice in
meters
Metric
2. Convert 3.4 grams to
Conversion
milligrams
3. Convert 1,234 milliliters to
The prefixes you
liters
must memorize
4. Convert 234 centimeters to
are as follows:
meters
kilo
= 1000x
5. Convert 1.0 deciliters to liters
hecto = 100x
6. Convert 0.024 liters to
deka = 10x
milliliters
deci = 1/10x
7. Convert 60 seconds to
centi = 1/100x
milliseconds
milli = 1/1000x
8. Convert 1.0 kilograms to
milligrams
Hydrogen bomb blast over
North Carolina, 1961
Aim 2 – Scientific Notation
Question: How do scientists express
large and small values in chemistry?
0.0000000000289
= 2.89 x 10-11
Scientific notation - allows us to easily
express large and small numbers
• A number in scientific notation is written as
follows:
M x 10n
• M is the _____________, 1< M < 10
• n is the ______________– the number of 10’s
we multiply or divide by
– n can be an integer that is positive, negative, or 0
– If n is positive – multiply by 10’s
– If n is negative – divide by 10’s
– If n is zero (100) – multiply or divide by 1
Converting to scientific notation
• Given the value: 6,020
• To change this to scientific notation, we must
determine the ______________________
that will give us a mantissa that is 1 < M < 10
• 6.02 is between 10 and 1
– We multiply 6.02 by ____________
– _____________________
– to get 6,020
– 1,000 = 103
• Therefore, ________________ is 6,020
converted to scientific notation
Converting to scientific notation
• Given the value: 0.0000345
• To change this to scientific notation, we must
by the number of 10’s that will give us a
mantissa that is 1 < M < 10
• 3.45 is between 10 and 1
– We divide 3.45 by _____________
or 10 x 10 x 10 x10 x 10 to get 6,020
– 1/100,000 = 10-5
• Therefore, ________________ is 0.0000345
converted to scientific notation
Converting scientific notation into numbers
• For positive exponents:
– Given the value:
7.8 x 104
– To change the scientific notation into a
number, simply multiply
7.8 x 10 x 10 x 10 x 10 = ______________
• For negative exponents:
– Given the value:
4.8 x 10-4
– To change the scientific notation into a
number simply divide
4.8 / (10 x 10 x 10 x 10) = _____________
Multiplying with scientific notation
• When multiplying numbers:
– ADD the exponents;
– MULTIPLY the mantissas,
– If need be, CHANGE the mantissa into a
value between 0 and 1
• Examples
a. (2.0 x 105) x (8.0 x 10-2)
= 16.0 x 103 = 1.60 x 103
b. (4.0 x 104) x (5.0 x 103)
= 20 x 107
= 2.0 x 108
Dividing with scientific notation
• When dividing numbers:
– SUBTRACT the exponents;
– DIVIDE the mantissas,
– If need be, CHANGE the mantissa into a
value between 0 and 1
• Examples
a. (6.0 x 105) / (3.0 x 10-2) = 2.0 x 107
b. (2.0 x 106) / (5.0 x 103)
= 0.4 x 103 = 4.0 x 101
Adding and subtracting with sci notation
• The exponents must be the same value
• Example:
– you cannot add 1.2 x 103 and 2.4 x 102
– You must convert the numbers so they
_______________________________
• Examples
a. (6.0 x 102) + (3.0 x 102) = 9.0 x 102
b. (2.0 x 103) + (5.4 x 105)
= (2.0 x 103) + (540 x 103) = 542 x 103
= 5.42 x 105
Practice in Scientific Notation
1.
2.
3.
4.
5.
6.
7.
8.
Write in scientific notation: 0.000467
Write in scientific notation: 32,000,000
Express 5.43 x 10-3 as a number.
Solve: (4.5 x 10-14) x (5.2 x 103) =
Solve: (6.1 x 105)/(1.2 x 10-3) =
Solve: (3.74 x 10-3) =
Solve: (4.4 x 102) + (6.2 x 102) =
Solve: (2.4 x 103) – (8.0 x 102) =
What is helium used for?
Aim 3 – Error in Chem
Question: How do we determine the
amount of accuracy in chemistry
experiments?
Hint:
what makes
Robin Hood
the best with
a bow?
Precision
• How close the measured values
_________________________.
• Which set of data below shows the best
precision in its measurements?
• Which set of data shows the worst precision?
Trial 1
Trial 2
Trial 3
Trial 4
Data Set Data Set Data Set
1
2
3
24
24.5
24.5
21
23.9
24.0
33
24.3
19.045
40
24.2
20.01
Data Set
4
24.5882
21.0892
40.2872
32.8452
Accuracy
• How close a measured value is to the
_______________________
• Which set of data below shows the best
accuracy in its measurements?
• Which set of data shows the worst accuracy?
Actual
Data Set Data Set Data Set Data Set
Value =
1
2
3
4
4.51
Trial 1
3.9
15.90
4.53
4.0588
Trial 2
4.1
15.89
4.49
21.089
Trial 3
4.0
15.88
4.52
40.287
Precision vs Accuracy
• Chemistry measurements seek to have both
__________________________________
• Some error does occur though; how do we
determine the error in our measurements?
• Table T – _________________________
Percent Error in accuracy
• To determine the percent error, use the
following formula found on Table T:
% error = Measured value – Accepted value x 100%
Accepted value
or % error = MV – AV x 100%
AV
• _____________________ – what the student,
scientist, or experiment determines as a value
• _____________________ – the theoretical,
actual, real, or true value
Percent Error in accuracy
• Example 1: A student determines the density of
a metal sample to be 3.4 g/mL. The accepted
value for the density is 3.0 g/mL. What is the
percent error in the student’s measurement?
% error = MV – AV x 100%
AV
% error =
% error =
% error =
Percent Error in accuracy
• Example 2: A researcher makes an error
collecting a gas in his experiment. He collected
only 605 mL of gas instead of the theoretical yield
of 650 mL. What is his percent error?
% error = MV – AV x 100%
AV
% error =
% error =
% error =
Practice – Error in Measurements
1. How much error is in an experiment where the
measured value is 10.0 mL but the accepted
value is 9.0 mL?
2. A gum manufacturer uses his latest supply of
gum ingredients to make 5,900 pieces of gum.
He was actually supposed to make 6,000 pieces
of gum. What is the percent error in his gum
yield?
3. The accepted value for a chemical’s boiling point
is 1,200oC. A scientist determines
experimentally that the boiling point is 1,150oC.
What is his percent error?
Aim 4 – Significant Figures
Question: How can we show how
precision our measurements are?
Significant figures
• the number of significant figures in a result is
simply the number of figures that are known
with some _______________________.
• Example:
– The number 13.2 is said to have
3 significant figures.
– The number 13.20 is said to have
4 significant figures.
• Significant figures allow us to show the level
of ____________________ in measurement
Real World examples:
• A manufacturer claims each pack of their
lollipops contains 20 lollipops.
• Accuracy:
– a sample of packets have
19, 20, 22, 18, 21,19,21 lollipops.
– The average is 20.
– __________________________________
• Precision:
– a sample of packets have
18, 17, 17, 17, 18, 18, 17 lollipops.
– The claim is not accurate, but the number of
lollipops in each bag __________________
Real World examples:
• While doing an experimental test in chemistry
with five trials, the end results of the five trials
the test are: 35 kg, 36 kg, 33 kg, 35 kg,
36 kg. The actual value (as found in a
scientific data book) is meant to be 42 kg.
– From the results, ____________________
_________________
– _________________ since the actual
value should be 42kg.
– _________________, since they do not
vary from each other.
Rules for determining significant figures
1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9)
are ALWAYS significant.
– 1.456
4 significant figures
– 2,298,356
7 significant figures
– 1,234.58
6 significant figures
2) ALL zeroes between non-zero numbers are
ALWAYS significant.
– 1.001
4 significant figures
– 2,200.4
5 significant figures
– 101
3 significant figures
Rules for determining significant figures
3) ALL zeroes which are SIMULTANEOUSLY
to the right of the decimal point AND at the
end of the number are ALWAYS
significant.
– 1.00
3 significant figures
– 1.00400
6 significant figures
4) ALL zeroes which are to the left of a
written decimal point and are in a
number > 10 are ALWAYS significant.
– 1,000
1 significant figure
– 410
2 significant figures
Rules for determining significant figures
• A helpful way to check rules 3 and 4 is to
write the number in scientific notation.
• If you can/must get rid of the zeroes, then
they are NOT significant.
• Examples: How many significant figures are
present in the following numbers?
– 1,010
3 significant figures
– 0.00040
2 significant figures
– 12,000
2 significant figures
– 100.0
4 significant figures
What is an "exact number"?
• Some numbers are exact because they are
known with complete certainty.
• Most exact numbers are integers:
– exactly _____________________
– exactly _____________________
– Exact numbers are often found as conversion
factors or as counts of objects.
• Exact numbers can be considered to have an
___________________________________
• The number of apparent significant figures in any
exact number can be ignored as a limiting factor
in determining the number of significant figures in
the ________________________________
Reporting measured quantities
In Summary
1. All non zero numbers are significant (1-9)
2. Zeros located between non zero
numbers are significant
3. Zeros used to place other numbers ARE
NOT significant figures
4. Zeros at the end of a number that
contains a decimal ARE significant
Aim 5:
How do we
calculate using
significant
figures?
Or,
why Mr. Foley
does not build
bridges
anymore
Darn it! I told
Foley to round to
the 1,000th place,
not the 10th!!!!
Calculations with Significant Figures
• When calculating using multiplication and
division:
– Answers can only have as many significant
figures as the number with the least
number of significant figures
• Ex 1. 4,040
How many sig figs?
3
x 20.
How many sig figs?
2
=
How many in answer? 3
=
How many sig figs should
be in the answer?
2
Calculations with Significant Figures
• Ex 2. 1,040
How many sig figs?
3
x 10.41
How many sig figs?
4
=
How many in answer? 6
=
How many sig figs should
be in the answer?
3
• Ex 3. 25,000.0 How many sig figs?
6
125
How many sig figs?
3
=
How many in answer? 1
=
How many sig figs should
be in the answer?
3
Calculations with Significant Figures
• Addition and Subtraction:
– Answer can have as many decimals
as the least number in the problem.
Ex1 40.108
+ 2.3
42.408
 42.4
Ex2 5,250.4
- 250.355
5,000.545
 5,000.5
Practice Calculations with Sig Figs
a) 2.34 x 12,000 = 28,000
b) 1.5 / 678
= 0.0022
c) 41.25 + 0.008 = 41.26
d) 41.25 – 1.2
= 40.
e) 0.500 – 0.23 = 0.27
f) 125,000 x 23 = 2,900,000
g) 34,000.0 / 23 = 1,500
h) 1.23 + 0.1004 = 1.33