Download 7.3 Scientific Notation NOTES

OBJECTIVE
THE STUDENT WILL BE
ABLE TO:
EXPRESS NUMBERS IN
SCIENTIFIC AND
DECIMAL NOTATION.
HOW WIDE IS OUR UNIVERSE?
210,000,000,000,000,000,000,000
miles
(22 zeros)
This number is written in decimal
notation. When numbers get this
large, it is easier to write them in
scientific notation.
7.3 SCIENTIFIC NOTATION
• A number written in scientific
notation is always in the form:
a ´ 10
n
• where 1 ≤ a < 10 and n is an
Standard Form to
Scientific Notation:
1)
2)
Move decimal point to the right of first
digit.
Number of spaces moved will be “n”
 If decimal is > 10, then
 If decimal is < 1, then
a ´ 10
-n
a ´ 10
n
EX 1: Convert to Sci Not
a) 4,062,000,000,000
b) 0.000000823
Scientific Notation to
Standard Form:
1) If n > 0, move decimal point
n spaces to the right, fill in with
zeros.
2) If n < 0, move decimal point
n spaces to the left, fill in with
zeros.
EX 2: Convert to Standard Form
a) 6.49 ×
b) 1.8 ×
5
10
−3
10
EX 3: Find the Product. Write
answer in BOTH forms.
(5 ×
−6
10 )(2.3
×
12
10 )
EX 4: Find the Quotient. Write
answer in BOTH forms.
4.5 ´ 10
3
1.5 ´ 10
8
HOW WIDE IS OUR UNIVERSE?
210,000,000,000,000,000,000,000
miles
(22 zeros)
This number is written in decimal
notation. When numbers get this
large, it is easier to write them in
scientific notation.
7.3 HW PG. 419
#1 – 19 ODDS
(10 PROBLEMS)
WHAT’S THE NUMBER?
30,000 × 10−1
3×
3
10
0.3 ×
P-12
4
10
SCIENTIFIC NOTATION OR NOT?
30,000 × 10−1
3 × 103
0.3 × 104
P-13
WHICH IS GREATER?
8×
4×
P-14
−3
10
−1
10
MATCHING CARD SET A
1. Take turns to match a card in scientific notation with a card in decimal notation.
2. Each time you match a pair of cards explain your thinking clearly and carefully.
Place your cards side by side on your desk, not on top of one another, so that
everyone can see them.
3. Partners should either agree with the explanation, or challenge it if it is not clear or
not complete.
4. It is important that everyone in the group understands the matching of each card.
5. You should find that two cards do not have a match. Write the alternative notation
for these measurements on the blank cards to produce a pair.
P-15