Learn to express large numbers in scientific notation'

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Learn to express large numbers in scientific
notation.
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Insert Lesson Title Here
Vocabulary
standard form scientific notation
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The distance from Venus to the Sun is over
100,000,000 kilometers. You can write this number
as a power of ten by using a base of ten and an
exponent.
10 10 10 10 10 10 10 10 108
Power of ten
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The table shows several powers of ten.
Power of 10
Meaning
Value
101
10
10
102
10 10
100
10 10 10
1,000
103
10 10 10 10
104
10,000
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Additional Example 1 Multiplying by Powers of Ten
Multiply 14 103.
Use 10 as a factor 3 times.
14 103 14 (10 10 10)
14 1,000
Multiply.
14,000
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Try This Example 1
Multiply 12 102.
Use 10 as a factor 2 times.
12 102 12 (10 10)
Multiply.
12 100
1,200
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You can also find the product of a number and a
power of ten simply by moving the decimal point
of the number. For powers of ten with positive
exponents, move the decimal point to the right.
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Additional Example 2 Multiplying by Powers of
Ten Mentally
Find each product.
A. 212 104
4 places
Move the decimal point 4 places.
212 104 212.0000
(You will need to add 4 zeros.)
2,120,000
B. 31.6 103
3 places
31.6 103 31.600
Move the decimal point 3 places.
31,600
(You will need to add 2 zeros.)
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Insert Lesson Title Here
Try This Example 2
Find each product.
A. 22.5 102
2 places
Move the decimal point 2 places.
22.5 102 22.50
(You will need to add 1 zero.)
2,250
B. 39.5 103
3 places
39.5 103 39.500
Move the decimal point 3 places.
39,500
(You will need to add 2 zeros.)
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Numbers are usually written in standard form. For
example, 17,900,000 is in standard form.
Scientific notation is a kind of shorthand that
can be used to write large numbers. Numbers
expressed in scientific notation are written as
the product of two factors. In scientific
notation, 17,900,000 is written as
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x 10
1.79
A power of 10
A number greater than or equal to 1 but less than
10
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Writing Math
In scientific notation, it is customary to use a
multiplication cross (?) instead of a dot.
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Additional Example 3A Writing Numbers in
Scientific Notation
Write the number in scientific notation.
A. 4,340,000
Move the decimal point to get a number that is
greater than or equal to 1 and less than 10.
4,340,000 4,340,000
The exponent is equal to the number of places
the decimal point is moved.
4.34 ? 106
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Additional Example 3B Writing Numbers in
Scientific Notation
Write the number in scientific notation.
B. 327,000,000
Move the decimal point to get a number that is
greater than or equal to 1 and less than 10.
327,000,000 327,000,000
The exponent is equal to the number of places
the decimal point is moved.
3.27 ? 108
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Insert Lesson Title Here
Try This Example 3A
Write the number in scientific notation.
A. 8,421,000
Move the decimal point to get a number that is
greater than or equal to 1 and less than 10.
8,421,000 8,421,000
The exponent is equal to the number of places
the decimal point is moved.
8.421 ? 106
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Insert Lesson Title Here
Try This Example 3B
Write the number in scientific notation.
B. 327,000
Move the decimal point to get a number that is
greater than or equal to 1 and less than 10.
327,000 327,000
The exponent is equal to the number of places
the decimal point is moved.
3.27 ? 105
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Additional Example 4 Writing Numbers in Standard
Form
The population of China in the year 2000 was
estimated to be about 1.262 ? 109. Write this
number in standard form.
Since the exponent is 9, move the decimal point 9
places to the right.
1.262 ? 109 1.262000000
1,262,000,000
The population of China was about
1,262,000,000 people.
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Insert Lesson Title Here
Try This Example 4
The distance from the Earth to the Sun is
calculated to be 1.5 ? 108 kilometers. Write this
distance in standard form.
Since the exponent is 8, move the decimal point 8
places to the right.
1.5 ? 108 1.50000000
150,000,000
The distance from the Earth to the Sun is about
150,000,000 kilometers.
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Insert Lesson Title Here
Lesson Quiz Part 1
Multiply.
2,500
1. 25 ? 102
2. 18 ? 104
180,000
Find each product.
3. 110 ? 102
11,000
4. 3.742 ? 103
3,742
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Lesson Quiz Part 2
Write each number in scientific notation.. 5.
7,400,000 6. 45,000 7. Earth is about 9.292 ?
107 miles from the Sun. Write this number in
standard form.
7.4 ? 106
4.5 ?104
92,920,000