Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Using Scientific Measurements
Accuracy and Precision
The terms accuracy and precision mean the same thing to most people
...
Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured
...
Thus, measured
values that are accurate are close to the accepted value
...


Percentage Error
The accuracy of an individual value or of an average experimental value can be compared quantitatively with the correct
or accepted value by calculating the percentage error
...

Percentage error = (Value experimental – Value accepted/ Value accepted) x100
Percentage error has a negative value if the accepted value is greater than the experimental value
...


Error in Measurement
Some error or uncertainty always exists in any measurement
...
The conditions of measurement also affect the outcome
...
Some balances can be read more precisely than others, the same is true of rulers, graduated cylinders, and
other measuring devises
...


Significant Figures
In science, measured values are reported in terms of significant figures
...
The term significant
does not mean certain
...

Insignificant digits are never reported
...
The significance of zeros in a number depends on their
location, however
...
Zeros appearing between nonzero digits are
significant
...
Zeros appearing in front of all nonzero
digits are not significant
...
Zeros at the end of a number and to the
right of a decimal point are significant
...
Zeros at the end of a number but to the left
of a decimal point may or may not be
significant
...
A decimal point placed
after zeros indicates that they are
significant
...
40
...
87 009 km has five significant figures
a
...
095 897 m has five significant figures
b
...
0009 kg has one significant figure
a
...
00 g has four significant figures
...
9
...
2000 m may contain from one to four significant
figures, depending on how many zeros are
placeholders
...

b
...
M contains four significant figures,
indicated by the presence of the decimal point
...
This is
especially true when you are using a calculator to carry out mathematical operations
...

If the digit following the last
digit to be retained is:
Greater than 5
Less than 5
5, followed by nonzero digit(s)
5, not followed by nonzero
digit(s), and preceded by an odd
5, not followed by nonzero digit
(s), and the preceding significant
digit is even

Then the last digit should:
Be increased by 1
Stay the same
Be increased by 1
Be increased by 1
Stay the same

Example (rounded to three
significant figures)
42
...
7 g
17
...
3 m
2
...
79 cm
4
...
64 kg
(because 3 is odd)
78
...
6 mL
(because 6 is even)

Addition or Subtraction with Significant Figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as
there are in the measurement having the fewest digits to the right of the decimal point
...


Scientific Notation
In scientific notation, numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1
but less than 10 and n is a whole number
...
Addition and subtraction
These operations can be performed only if the values have the same exponent (n
factor)
...
Once the
exponents are equal, the M factors can be added or subtracted
...
Consider the example of the addition of 4
...
9 x 103 kg
...

4
...
79 x 104 kg
4
...
0 x 104
Note that the units remain kg throughout
2
...

Consider the multiplication of 5
...
1 x 10-2+ um
...
23 x 106um) (7
...
23 x 7
...
133 x 104 x 10-2 (adjust to two significant digits)
= 3
...
Division
The M factors are divided, and the exponent of the denominator is subtracted from that of
the numerator
...
44 x 107 g = 5
...
1 x 104 mol
8
...
6716049383 x 103 (adjust to two significant figures)
= 6
...


Using Sample Problems
Learning to analyze and solve such problems requires practice and a logical approach
Analyze: The first step in solving a quantitative word problem is to read the problem carefully at least twice and to
analyze the information in it
...

Compute: The third step involves substituting the data and necessary conversion factors into the plan you have developed
...
Use the following methods, when appropriate, to
carry out the evaluation
...
Check to see that the units are correct
...
Are the conversion factors
correct?
2
...
Compare the estimate
with your actual result
...

3
...
Does it seem reasonable compared with the values given in the
problem? If y calculated the density of vegetable oil and got a value of 54
...
Oil floats on water therefore its density is less than water, so the value obtained should
be less than 1
...

4
...


Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value
...
As the masses of the samples increase, their volumes increase by the same factor
...
Halving the mass halves the volume
...
” The general equation for a directly proportional relationship between the two
variables can also be written as follows
...
Written in this form, the equation expresses an important
fact about direct proportion: the ratio between the variables remains constant
...

y = kx
The equation y = kx may look familiar to you
...
The mass and volume of a pure substance are
proportional to each other
...
The constant
two variables is density
...


straight line
...
An example of an inversely
proportional relationship is that between speed of travel and the time required to cover a fixed distance
...
Halving the speed doubles the required time
...

y = 1/x
This is read “y is proportional to 1 divided by x
...

xy = k
In the equation, k is the proportionality constant
...

A graph of variables that are inversely proportional produces a curve called a hyperbola

---