Download Ex. 19: 3.1 x 10

M60 Section 3.1: Scientific Notation for Positive Numbers
Review: Exponents: Short hand way of expressing _________________________ ________________
Ex. 1:
53
In the expression:
3 is the _______________ and 5 is the ______________. The exponent tells us how
many times to use the ___________ as a factor in ______________ ____________.
Use of Exponents:
Area of a Square:
Volume of a Cube:
Ex. 2: In the sentence:
2, 3, and 5 are called _____________and 30 is called the ______________
Ex. 3: In the sentence: 5 + 7 + 2 = 14
5, 7, and 2 are called ______________ and 14 is called the ____________
Ex. 4:
Ex. 5:
Ex. 6: Write in exponential form:
(-7)(-7)(-7)(-7) =
Ex. 7: Use correct notation to described the opposite of 4²
Part A: Exponents and Powers of 10
Multiplication and Division of positive numbers by powers of 10:
Ex. 8:
42.3 x 10 4 =
Ex. 9:
Ex. 10:
0.025 x 10 6 =
Ex. 11:
Ex. 12:
3, 000
=
100
Ex. 13:
6.2 x 10 9 =
40
=
10
432 100
=
1000
So, multiplication and division by powers of 10 really means keeping track of the ______________ or the
Movement of the decimal __________________.
M60, Sec. 3.1 pg.2
Part B: Standard Notation vs. Scientific Notation with Large Positive Numbers:
Standard Notation: "regular" numbers. The way we usually see numbers written:
ex:
7,340
2.6
261,000
Scientific Notation:
Useful for very large numbers where the power on 10 shows the magnitude of
a number. It consists of a number that has exactly one nonzero digit to the left of the decimal (It could
be a negative number, but we'll concentrate on positive ones first.) multiplied by some power of 10.
a x 10 b
where
(The extreme value of a is between 1 and 10)
ex: distance within the solar system, national debt (currently $14,600,000,000,000), board feet
production of lumber in a year,
ex:
4.26 x 10 3
STANDARD FORM
and
7.4 x 10 5
SCIENTIFIC NOTATION
Ex. 14: 2300
Ex. 15: 400
Ex. 16: 4270
Ex. 17: 9,273,000
Ex. 18:
2.37 x 10 4
Ex. 19:
3.1 x 10
Ex. 20:
4 x 10 5
Ex. 21:
9.6 x 10 2
M60, Sec. 3.1 pg.3
Part C: Standard Notation vs. Scientific Notation and Small Positive Numbers:
Ex: microscopic bacteria, medications, computer chip resistors
STANDARD NOTATION
SCIENTIFIC NOTATION
Ex. 22: 0.000392
Ex. 23: 0.001234
Ex. 24: 0.2376
Ex. 25: 0.00295
Ex. 26:
6.2 x 10 –2
Ex. 27:
3.72 x 10 –3
Ex. 28:
4.55 x 10 –5
Ex. 29: Write the following in scientific notation:
16 x 10⁵
In summary: For scientific notation of positive numbers:
A positive exponent on the 10 means the number is __________ than 1. Think of it as a
_____________ number. A negative exponent on the 10 means the number is less than______ . Think
of it as a number very close to ________. In other words a _________.
M60, Sec. 3.1 pg.4
Part D: Multiplying Positive Numbers in Scientific Notation:
Look at multiplying the following:
=
Product Rule of Exponents:
When multiplying the same base, ___________ the base and __________ the exponents
Ex. 29: Use the Product Rule of Exponents to multiply the following numbers.
a)
b)
c)
Ex. 30: Use the commutative property of multiplication to rewrite the following and then multiply using
your calculator to find a, and the product rule of exponents to find b.
a)
b)
c)
Part E: Applications of Scientific Notation:
A song typically uses
bytes of storage on an mp3 player. Use scientific notation and
multiplication to determine how large a player you would need to store the 1600 cover versions of the
song “Yesterday”.