Today’s Topics:
•Set Notation
•Intersections of Sets
•Unions of Sets
•Converting between Decimal and
Scientific Notations
Set notation is a tool that allows the writer to list a
collection of letters or numbers (called elements) as
members of the same group.
The Roster Method of representing sets denotes a complete
list of a set’s elements separated by commas and contained
within braces.
Here’s an example: {b, f, m, p, v, w}
This is the best method to use when sets are finite and small.
Note: Sometimes a writer must state that there are no
elements in a set. This is called the empty set, which we
represent with this symbol: Ø
Intersections of Sets:
“What is the intersection of these sets?” is the same question as
“Which elements do these sets have in common?”
Question: {1, 2, 3} ∩ {2, 4, 6}
Answer: {2}
Question: {a, b, e, f} ∩ {b, f, g}
Answer: {b, f}
Sometimes the sets have no elements in common
Question: {4, 5, 6} ∩ {8, 9. 10}
Answer: Ø
Unions of Sets:
“What is the union of these sets?” is the same question as “What is the
complete list of all the elements contained in both sets altogether?”
Note: If an element appears in both sets, it does NOT need to be listed
twice in the union set.
Question: {p, a, r, k} U {d, r, i, v, e}
Answer: {p, a, r, k, d, i, v, e}
Notice in the answer that the element r is only listed once in the answer.
Question: {2, 4, 5, 7} U {1, 3, 5}
Answer: {1, 2, 3, 4, 5, 7}
Again, the element 5 is only listed once in the answer.
In Decimal Notation (how number values are most commonly written), very large
and very small numbers require a long series of zeros to denote.
For example:
0.00000000237
and
1,367,000,000,000
Scientific Notation was invented so that numbers of very large or very small size
could be written with fewer symbols.
Here are the above numbers in scientific notation:
2.37 x 10-9
and
1.367 x 1012
Notice that the very small number on the left (0.00000000237) is associated with
a negative exponential power of ten in its scientific notation (-9).
Conversely, the very large number on the right (1,367,000,000,000 ) is
associated with a positive exponential power of ten in its scientific notation (12).
This correlation always holds true in these conversions.
To Convert from Decimal (Normal) Notation to Scientific Notation:
A)
0.000000408
Take the decimal and move it to the right of the first non-zero digit you pass.
Like this:
0 0000004.08
You moved it seven places right to obtain the number 4.08
Since the value itself (0.000000408) is actually very small, we use negative
exponent in our final answer:
4.08 x 10 -7
B)
120,500
Take the decimal (which is unseen on the far right) and move it to the left until there
is only one non-zero digit left. Like this
120 500.
becomes
1.20500
You moved it five places to the left to obtain the number 1.205
Since the number itself (120,500) is actually very large, we use a positive exponent
in our final answer:
1.205 x 105
To Convert from Scientific Notation to Decimal (Normal) Notation:
C) 7.035 x 106
This exponent is positive (6), which means that the actual number is very large. So,
we should move the decimal to the RIGHT to make the value larger. The
exponent tells us how many places right we should go: six
Starting with 7.035 and moving right six places we get 7 035_ _ _ .
Moving the decimal in this way leaves us with empty spaces. We fill them in with
zeros to obtain our final answer: 7035000
Or, if you prefer: 7,035,000
D) 8.65 x 10-2
This exponent is negative (-2), which means the actual number is very small.
So, we should move the decimal to the LEFT to make the value smaller.
The exponent tells us how many places left we should go: two
Starting with 8.65 and moving left two places we get . _ 865
Again, moving the decimal in this way leaves us with empty spaces. Again, we fill
them in with zeros to obtain our final answer: .0865
Or, if you prefer: 0.0865
Don’t forget to include the four elements required for all textbook assignments!
What are they?
1. Directions
2. Questions
3. Work
4. Answers
Today’s Assignment:
Pg. 14 # 21-34
and
Pg. 26 # 65-86