Download Operations with Scientific Notation

Operations with
Scientific Notation
2.4
Adding and
Subtracting
Numbers
Numbers in scientific notation can
be added or subtracted directly or by
rewriting them in standard notation
Example 1: The
table shows the
population of
the three largest
countries in
North America in
2011. Find the
total population
of these
countries.
Country
United States
Canada
Mexico
Population
3.1 x 108
3.38 x 107
1.1 x 108
METHOD 1:
Step 1: Write each population with the same
power of 10
Country
United States
Canada
Mexico
Population
3.1 x 108
0.338 x 108
1.1 x 108
Step 2: Add the multipliers for each population
3.1 + 0.338 + 1.1 = 4.538
Step 3: Write the final answer in scientific
notation
4.538 x 108
Example 1:The
table shows the
population of
the three largest
countries in
North America in
2011. Find the
total population
of these
countries.
Country
United States
Canada
Mexico
Population
3.1 x 108
3.38 x 107
1.1 x 108
 METHOD 2:
 Step 1: Write each number in standard notation
Country
United States
Canada
Mexico
Population
310,000,000
33,800,000
110,000,000
 Step 2: Find the sum of the numbers in
standard notation
 310,000,000+ 33,800,000 + 110,000,000 =
453,800,000 .
 Step 3: Write the answer in scientific notation
8
 4.538 x 10
Example 2:
Combine the
following
numbers and
write the sum
in scientific
notation
1.2 x 10 4
2.5 x 105
Method 1:
Method 2:
0.12 x 105 + 2.5x 105
2.5 + 0.12 = 2.62
 12,000 + 250,000 = 262,000
5
2.62 x 10
2.62 x 105
Your turn:
Which
method will
you choose?
Turn to page 52 in your textbook and
complete #1 “Your Turn”
Step 1: Multiply the coefficients
Multiplication and
Division with
Scientific
Notation
Example
(5.1 x 10 4)(2.3 X 106)
5.1 x 2.3 =
11.73
Step 2: Add the powers of 10: 4+6 =
10
Step 3: Check to be sure the product
is in scientific notation
11.73 x 1010 = 1.173 x 1011
Step 1: Multiply the coefficients
 2.8x 5.1=
 14.28
Practice
problem
(2.8x 103)(5.1 x 10 -7)
Step 2: Add the powers of 10:
 3+ (-7) =
 -4
Step 3: Check to be sure the product is
in scientific notation
 14.28 x 10-4 = 1.428 x 10-3
 Step 1: Divide the coefficients
Dividing
Numbers in
Scientific
Notation
3.9𝑥108
6.5 𝑥 10 − 4
 3.9 ÷ 6.5 =
 0.6
 Step 2: subtract the powers of 10
 8-(-4)
 12
 Step 3: Check to be sure the quotient is in
scientific notation
 0.6 x 1012
 6 x 1011
Turn to page
52 in your
textbook and
complete # 2-3
“Your Turn”