Download 1 Date: 4-17-12 Topic: 7-10 Scientific Notation Essential Question

Date: 4-17-12
Essential Question: What is scientific notation?
Topic: 7-10
Scientific Notation
Objective:
To use scientific notation.
Some numbers are so large or so small that they are difficult to
read or to write. For example, consider the following
measurements:
diameter of the solar system:
118,000.000,000 km
diameter of a silver atom:
0.00000000000025 km
Scientific notation makes it easier to work with such numbers.
To write a positive number in scientific notation, you express
it as the product of a number greater than or equal to 1 but less
than 10 and an integral power of 10. Study the following
examples.
Number
118,000,000,000
Number Written
in Scientific
Notation
Movement of
the Decimal
Point
11 places
11 places
4,709,000,000
9 places
9 places
0.000152
4 places
4 places
0.00000000000025
13 places
13 places
Summary
1
Notice that when a positive number greater than or equal to 10
is written in scientific notation, the power of 10 used is
positive. When the number is less than 1, the power of 10 used
is negative.
Example 1:
Write each number in scientific notation.
a.
10 places
Move the decimal point left 10 places to get a
number between 1 and 10.
b.
7 places
Move the decimal point right 7 places to get a
number between 1 and 10.
Exercise 1:
Write each number in scientific notation.
a.
b.
2
Example 2:
Write each number in decimal form
a.
8 places
b.
5 places
Exercise 2:
Write each number in decimal form
a.
b.
c.
d.
e.
3
Numbers written in scientific notation can be multiplied and
divided easily by using the rules of exponents.
Example 3:
Simplify. Write your answers in scientific notation.
a.
b. (
)(
)
(
)(
(
)
(
(
)
(
)
)
)
c.
(
)(
)
4
Exercise 3:
Simplify. Write your answers in scientific notation. DO NOT
use a calculator. Show your work.
a. (
)(
b. (
)(
)
)
c.
d.
e.
f.
(
)(
)
5
Example 4:
The distance from the sun to Mercury is approximately
The distance from the sun to Pluto is approximately
Find the ratio of the first distance to the second.
km.
km.
6
Exercise 4:
The distance from the sun to the earth is approximately
km. The distance from the sun to nearest star, Alpha
Centauri, is approximately
km. Find the ratio of the
first distance to the second. DO NOT use a calculator. Show
your work. Leave your answer in fractional form.
7
Our decimal number system is based on powers of 10.
Example 5:
Write each number in expanded notation using powers of 10.
a.
b.
c.
Exercise 5:
Write each number in expanded notation using powers of 10.
a.
b.
c.
d.
e.
f.
8
The metric system is also based upon powers of 10. To change
from one metric unit to another, you simply multiply by a
power of 10.
Example 6:
Complete each statement by writing a power of 10.
a. 1 km =
?
m
To change from kilometers to meters, multiply by
103.
b. 1 mL =
?
L
To change from milliliters, liters by 103.
Exxercise 6:
Complete each statement by writing a power of 10.
a. 1 kg =
?
b. 1 g =
?
kg
c. 1 m =
?
cm
d. 1 cm =
e. 1 g =
f. 1 mg =
Homework:
g
?
?
m
mg
?
g
P 339: 2-30, multiples of 4
P 340: problem 2
9