Day 1
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For Learning to Happen:
•Remove all other thoughts from your mind.
•Pay close attention.
•You have 3 Study Guides today so do NOT
waste class time….be respectful!
•Try all the examples.
•Ignore all other distractions.
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1
Exponents of Ten
What Is the Standard Form?
2
100
10
3
10
4
10
5
10
1,000
10,000
100,000
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Exponents of Ten
Notice that the number of zeros
matches the exponent number
102
103
104
105
100
1,000
10,000
100,000
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2
Multiply These Numbers
100 x 2 =
200
1,000 x 3 =
3,000
10,000 x 7 = 70,000
100,000 x 9 = 900,000
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Did you notice that all you have to do is multiply
1 x whole number & add the zeros behind?
100 x 2 =
200
1,000 x 3 =
3,000
10,000 x 7 = 70,000
100,000 x 9 = 900,000
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3
Short Cut for Writing Large Numbers
Combine these two steps for
writing large numbers.
2
6 x 10 = 600
6 x (10 x 10) = 6 x 100 = 600
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Short Cut for Writing Large Numbers
Remember!
The exponent is the same as
the number of zeros.
2
6 x 10 = 600
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4
Scientists often write very large
numbers in scientific notation using
positive exponents which consists of
two factors.
1st Factor: a number less than 10. But
greater than one.
2nd Factor: a power of ten.
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What is the number in Standard Form?
2
7 x 10 = 700
1st Factor:
2nd Factor:
a number less
a power of ten
than 10. But
greater than one
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5
Standard Form
Exponent Form
is when the number is when the number
is written out.
is written in
Scientific Notation
Example
Example
500
5 x 102
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What is the number in Standard Form?
3
8 x 10 = 8,000
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6
What is the number in Standard Form?
4
9 x 10 = 90,000
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What is the number in Standard Form?
2
4 x 10 = 400
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7
What is the number in Exponent Form?
500 = 5 x 10
2
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What is the number in Exponent Form?
3
6,000 = 6 x 10
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8
What is the number in Exponent Form?
4
90,000 = 9 x 10
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What is the number in Exponent Form?
5
700,000 = 7 x 10
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9
Scientists use scientific notation to
write really large numbers. This is
done with positive powers of ten.
They also use scientific notation to
write very small numbers.This is
done with negative powers of ten.
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The volume of earth is 259,000,000,000 mi3
1) Add a decimal after the first number.
.
2 59
2) Count how many places there are after the
decimal point.
2.59 000 000 000 = 11 places
3) Write the decimal place as a power of ten.
= 2.59 x 10 11
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10
Examples:
234,000
= 2.34×105
5 jumps right
0.0053
= 5.3 ×10−3
3 jumps left
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Large Numbers
31,000
4
×
10
=
3.1
4 jumps right
6,879,100
= 6.8791 ×106
6 jumps right
Positive Exponents move to the right
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11
Small Numbers
0.000528 = 5.28 ×10−4
4 jumps left
0.000009 = 9.0 ×10−6
6 jumps left
Negative Exponents move to the
left
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Write in Scientific Notation
1) 3,300,000 = 3.3 ×106
6 jumps right
2) 0.00062
= 6.2 ×10−4
4 jumps left
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12
Write in Standard Form
1) 3.6 × 105
3.60000
2) 5.83 × 10 −6
0 000005.83
360,000
0.00000583
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Take Out Your Study Guide!!!
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13
#1
Using Scientific Notation
Scientists use scientific notation to write
really large numbers. This is done with
positive powers of ten.
80,000,000,000 = 8 ×1010
10 jumps right
They also use scientific notation to write
very small numbers. This is done with
negative powers of ten.
0.0000003 = 3 ×10 −7
7 jumps left
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#2
Standard & Exponent Form
Standard Form is when the number is written out.
Example: 8, 200
Exponent Form is when the number is written in
Scientific Notation (a number times a power of 10)
Example: 8.2 x 103
Exponent Form 8.2 × 103
8.200
Standard Form = 8,200
103 = 1000
8.2 x 1000
= 8, 200
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14