Download Ch. 1.9

WARM UP
Calculate:
1.
3.1  10 =
31
2.
5.4  10 =
0.54
3.
=
1,000,000
4.
=
0.0001
5.
6.
=
SCIENTIFIC
NOTATION
S
OBJECTIVES
S To convert between scientific and standard notation
S To use scientific notation in multiplication and division
S To use scientific notation in approximating and estimating
S To work problems involving large numbers easily
DEFINITION
S Scientific notation for a number is notation of
the form a x 10 where 1 ≤ a < 10 and n is an
integer.
INTRODUCING THE CONCEPT
S Scientific notation is useful for calculating with very large or
very small numbers.
S It is also helpful for estimating
S Scientific notation for 2,800,000,000 miles, the distance from
the planet Neptune to the sun is
.
S For 0.000000022 cm. the diameter of a helium atom, it is
S For 100 it is
.
CONVERSIONS
S We can convert to scientific notation by multiplying by 1,
choosing
for the number 1, where b is the number
of decimal places to be moved.
S Example:
Write scientific notation for 20,000,000 degrees Kelvin, the
temperature near the sun’s center.
We need to move the decimal point 7 places to the left, so that it
is between the digits 2 and 0, so we choose
for 1 and
then multiply.
Multiplying by 1
Using the associative property
MORE EXAMPLES
S The wavelength of a certain red light is 0.000066 cm. Write
scientific notation for this number.
We need to move the decimal point 5 places to the right. We
choose
for 1, and then multiply.
Multiplying by 1
Using the associative property
MORE EXAMPLES
S Light travels about 9,460,000,000,000 km. in one year. Write
scientific notation for this number.
Multiplying by 1
moved the decimal point 12 places to the left
TRY THIS….
1. Convert 460,000,000,000 to scientific notation.
2. Convert 0.000000001235 to scientific notation.
3. The mass of a hydrogen atom is 0.0000000000000000000000017
grams. Write scientific notation for this number.
4. The distance from Earth to the sun is about 150,000,000 km.
Write scientific notation for this number.
EXAMPLES
S Convert to standard notation:
Moving the decimal point 5 places to the right.
Moving the decimal point 8 places to the left.
MULTIPLYING
S To multiply and divide using scientific notation, we use the
commutative and associative properties and then use the
properties of exponents to simplify the powers of ten.
Multiply and write the scientific notation for the answer:
We apply the commutative and associate properties:
We convert 13.95 to scientific notation and then simplify:
DIVIDING
Divide and write the scientific notation for the answer:
Factoring
Dividing
Converting 0.9 to
scientific notation
TRY THIS….
Multiply or divide write the scientific notation for the answer:
1.
2.
3.
ESTIMATING AND
APPROXIMATING
S Scientific notation is helpful in estimating or approximating.
Such estimating is an important skill in problem solving.
Estimate 780,000,000 x
Converting to scientific notation
& multiplying
Regrouping
Rounding
Rounding
Converting to
scientific notation
TRY THIS….
Estimate. Answer may vary depending on how you round:
CH. 1.9 HOMEWORK
Textbook pg. 47 #2 – 40 every other even