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and
Scientific
Notation
7-2
Powers
and
Scientific
Notation
7-2 Powers
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
Algebra 1Algebra 1
Holt
7-2 Powers of 10 and Scientific Notation
Warm Up
Evaluate each expression.
1. 123  1,000
123,000
2. 123  1,000
0.123
3. 0.003  100
0.3
4. 0.003  100
0.00003
5. 104
10,000
6. 10–4 0.0001
7. 230 1
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Objectives
Evaluate and multiply by powers of 10.
Convert between standard notation and
scientific notation.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Vocabulary
scientific notation
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
The table shows relationships between
several powers of 10.
Each time you divide by 10, the exponent
decreases by 1 and the decimal point moves
one place to the left.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
The table shows relationships between
several powers of 10.
Each time you multiply by 10, the exponent
increases by 1 and the decimal point moves
one place to the right.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Example 1: Evaluating Powers of 10
Find the value of each power of 10.
A. 10–6
B. 104
C. 109
Start with 1
and move the
decimal point
six places to
the left.
0.000001
Start with 1
and move the
decimal point
four places to
the right.
10,000
Start with 1
and move the
decimal point
nine places to
the right.
1,000,000,000
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Writing Math
You may need to add zeros to the right or left of
a number in order to move the decimal point in
that direction.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 1
Find the value of each power of 10.
a. 10–2
b. 105
c. 1010
Start with 1
and move the
decimal point
two places to
the left.
0.01
Start with 1
and move the
decimal point
five places to
the right.
100,000
Start with 1
and move the
decimal point
ten places to
the right.
10,000,000,000
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Reading Math
If you do not see a decimal point in a number, it
is understood to be at the end of the number.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Example 2: Writing Powers of 10
Write each number as a power of 10.
A. 1,000,000
B. 0.0001
C. 1,000
The decimal
point is six
places to the
right of 1, so the
exponent is 6.
The decimal
point is four
places to the
left of 1, so the
exponent is –4.
The decimal
point is three
places to the
right of 1, so the
exponent is 3.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 2
Write each number as a power of 10.
a. 100,000,000
b. 0.0001
c. 0.1
The decimal
point is eight
places to the
right of 1, so the
exponent is 8.
The decimal
point is four
places to the
left of 1, so the
exponent is –4.
The decimal
point is one
place to the
left of 1, so the
exponent is –1.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
You can also move the decimal point to find
the value of any number multiplied by a
power of 10. You start with the number
rather than starting with 1.
Multiplying by Powers of 10
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Example 3: Multiplying by Powers of 10
Find the value of each expression.
A. 23.89  108
23.8 9 0 0 0 0 0 0
2,389,000,000
Move the decimal point 8
places to the right.
B. 467  10–3
467
0.467
Holt McDougal Algebra 1
Move the decimal point 3
places to the left.
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 3
Find the value of each expression.
a. 853.4  105
853.4 0 0 0 0
85,340,000
Move the decimal point 5
places to the right.
b. 0.163  10–2
0.0 0163
0.00163
Holt McDougal Algebra 1
Move the decimal point 2
places to the left.
7-2 Powers of 10 and Scientific Notation
Scientific notation is a method of writing
numbers that are very large or very small. A
number written in scientific notation has two
parts that are multiplied.
The first part is a number that is greater than or equal
to 1 and less than 10.
The second part is a power of 10.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Example 4A: Astronomy Application
Saturn has a diameter of about
Its distance from the Sun is about
1,427,000,000 km.
km.
Write Saturn’s diameter in standard form.
120000
120,000 km
Holt McDougal Algebra 1
Move the decimal point 5 places to
the right.
7-2 Powers of 10 and Scientific Notation
Example 4B: Astronomy Application
Saturn has a diameter of about
Its distance from the Sun is about
1,427,000,000 km.
km.
Write Saturn’s distance from the Sun in
scientific notation.
Count the number of places
1,427,000,000
you need to move the
decimal point to get a
1,4 2 7,0 0 0,0 0 0
number between 1 and 10.
9 places
1.427  109 km
Holt McDougal Algebra 1
Use that number as the
exponent of 10.
7-2 Powers of 10 and Scientific Notation
Reading Math
Standard form refers to the usual way that
numbers are written—not in scientific notation.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 4a
Write Jupiter’s diameter in scientific notation.
143,000 km
143000
5 places
1.43  105 km
Holt McDougal Algebra 1
Count the number of places
you need to move the
decimal point to get a
number between 1 and 10.
Use that number as the
exponent of 10.
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 4b
Write Jupiter’s orbital speed in standard form.
13000
13,000 m/s
Holt McDougal Algebra 1
Move the decimal point 4 places to
the right.
7-2 Powers of 10 and Scientific Notation
Example 5: Comparing and Ordering Numbers in
Scientific Notation
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
Step 2 Order the numbers that have the same
power of 10.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Check It Out! Example 5
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014,
4.5  1030
Step 2 Order the numbers that have the same
power of 10.
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Lesson Quiz: Part I
Find the value of each expression.
1.
3,745,000
2.
0.00293
3. The Pacific Ocean has an area of about 6.4 х 107
square miles. Its volume is about 170,000,000
cubic miles.
a. Write the area of the Pacific Ocean in standard
form.
b. Write the volume of the Pacific Ocean in scientific
notation. 1.7  108 mi3
Holt McDougal Algebra 1
7-2 Powers of 10 and Scientific Notation
Lesson Quiz: Part II
4. Order the list of numbers from least to
greatest
Holt McDougal Algebra 1