Powers of 10 and Scientific Notation

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Powers of 10 and Scientific Notation
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
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Warm Up Evaluate each expression. 1. 123 ?
1,000 2. 123 ? 1,000 3. 0.003 ? 100 4. 0.003 ?
100 5. 104 6. 104 7. 230
123,000
0.123
0.3
0.00003
10,000
0.0001
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Objectives
Evaluate and multiply by powers of 10. Convert
between standard notation and scientific
notation.
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Vocabulary
scientific notation
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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.
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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.
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Example 1 Evaluating Powers of 10
Find the value of each power of 10.
C. 109
A. 106
B. 104
Start with 1 and move the decimal point six
places to the left.
Start with 1 and move the decimal point four
places to the right.
Start with 1 and move the decimal point nine
places to the right.
1,000,000,000
10,000
0.000001
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Check It Out! Example 1
Find the value of each power of 10.
a. 102
c. 1010
b. 105
Start with 1 and move the decimal point two
places to the left.
Start with 1 and move the decimal point five
places to the right.
Start with 1 and move the decimal point ten
places to the right.
10,000,000,000
100,000
0.01
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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.
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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.
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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.
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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
Move the decimal point 8 places to the right.
2,389,000,000
B. 467 ? 103
Move the decimal point 3 places to the left.
4 6 7
0.467
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Check It Out! Example 3
Find the value of each expression.
a. 853.4 ? 105
Move the decimal point 5 places to the right.
853.4 0 0 0 0
85,340,000
b. 0.163 ? 102
Move the decimal point 2 places to the left.
0.0 0163
0.00163
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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.
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Example 4A Astronomy Application
Saturn has a diameter of about km.
Its distance from the Sun is about 1,427,000,000
km.
Write Saturns diameter in standard form.
Move the decimal point 5 places to the right.
1 2 0 0 0 0
120,000 km
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Example 4B Astronomy Application
Saturn has a diameter of about km.
Its distance from the Sun is about 1,427,000,000
km.
Write Saturns distance from the Sun in
scientific notation.
Count the number of places you need to move the
decimal point to get a number between 1 and 10.
1,427,000,000
1,4 2 7,0 0 0,0 0 0
9 places
Use that number as the exponent of 10.
1.427 ? 109 km
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Check It Out! Example 4a
Use the information above to write Jupiters
diameter in scientific notation.
Count the number of places you need to move the
decimal point to get a number between 1 and 10.
143,000 km
1 4 3 0 0 0
5 places
Use that number as the exponent of 10.
1.43 ? 105 km
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Check It Out! Example 4b
Use the information above to write Jupiters
orbital speed in standard form.
1 3 0 0 0
Move the decimal point 4 places to the right.
13,000 m/s
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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
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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
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Lesson Quiz Part I
Find the value of each expression. 1. 2. 3.
The Pacific Ocean has an area of about 6.4 ? 107
square miles. Its volume is about 170,000,000
cubic miles. a. Write the area of the Pacific
Ocean in standard
3,745,000
0.00293
form.
b. Write the volume of the Pacific Ocean in
scientific notation.
1.7 ? 108 mi3
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Lesson Quiz Part II
Find the value of each expression.
4. Order the list of numbers from least to
greatest