Download 04-04 7.3 Multiplying and Dividing Decimals

§7.3 Multiplying and
Dividing Decimals
04/04/17
Today We’ll Discuss
How do we multiply and divide decimals
using fractions?
How do we multiply and divide decimals
using algorithms?
How do we use division to write
repeating decimals?
How do we use scientific notation?
Multiplication of Decimals
Think about decimals as fractions.
Now remember that in multiplying
decimals, we move the decimal point in
the answer.
Why? How can we explain this to students?
Multiplication of Decimals by
Converting to Fractions
A decimal stands for a fraction with a
power of 10.
We can simply convert our decimals back
to fractions and multiply the old way.
Example
Multiply each by first converting to
fractions.
a) 3 • 2.1
b) 2.5 • 1.34
Algorithm for Multiplying
Decimals
To multiply decimals…
1) Multiply as usual using your favorite
algorithm, ignoring decimal points.
2) Count the number of digits right of the
decimal point in each number.
3) Insert a decimal point in your answer,
ensuring that there are (2) many digits to the
right of it.
Example
Multiply each using the algorithm.
a) 0.26 • 4.8
b) 23.45 • 0.0062
Division of Decimals by
Converting to Fractions
Of course, we could take the long way
with division as well and convert to
fractions before dividing.
Let’s convert decimals to fractions and
see what happens.
Algorithm for Dividing Decimals
1) Multiply the divisor and dividend by a power of 10 so
that the divisor is a whole number.
2) Divide the usual way.
3) BUT! Instead of finding a remainder, continue the
division process on and on by placing 0’s to the right of
the dividend.
4) Stop when either you get 0 from the subtraction with
nothing left to bring down OR you see a pattern.
5) Place the decimal point in the quotient above the
one in the dividend.
Example
Find each quotient.
a) 2.8 ÷ 8
b) 7.5 ÷ 1.25
c) 2.5875 ÷ 2.5
PAST-CAM
●ON
Terminating vs. NonTerminating Decimals
There are three main kinds of decimals:
1) Terminating
2) Non-Terminating, Repeating
3) Non Terminating, Non-Repeating
PAST-CAM
●ON
Terminating Decimals
There are 2 ways to write these fractions
as terminating decimals.
A) Rewrite the fraction so that its
denominator is a power of 10
B) Divide the numerator by the
denominator (mostly saved for §7.3)
Fraction to Decimal Conversion
We can now convert all fractions to
decimals using long division.
Hooray!
Example
Write each fraction as a decimal.
Scientific Notation
Definition: A decimal is written in
scientific notation when it is written in
the form
where
number.
and
is a whole
The number a is called the mantissa,
while n is the characteristic.
Example
Rewrite each number using scientific
notation.
a) The average distance from Earth to the
Sun is about 150,000,000 km.
b) The distance from Earth to the nearest
star, Proxima Centauri, is about
40,000,000,000,000 km.
Example
Rewrite each number in standard form.
a) 1.245 × 109
b) 3.06 × 105
Example
How many times greater is the distance
from Earth to Proxima Centauri than from
Earth to the Sun?
Example
There are about 1.2 × 108 households in the
United States. The mean income per
household is about $7.0 × 104. What is the
total household income in the United
States? Write your answer in standard
notation.
Example
Complete each operation. Be sure your
answer is in scientific notation.
a) (3.5 × 109)(5 × 1010)
b) (5.4 × 1012)÷(9 × 106)
Homework #18 - §7.3
Pages 272-275
#10, 12 (use your noggin), 18, 20, 22,
24, 26, 28, 30, 32