Download Basic Concepts needed for Chemistry

Scientific Notation
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Scientists have developed a shorter method to
express very large numbers. This method is called
scientific notation. Scientific Notation is based on
powers of the base number 10.
The number 123,000,000,000 in scientific notation
is written as 1.23 x 1014
The number 0.00000508 in scientific notation is
written as 5.08 x 10-6
There is a significant advantage to writing very
large or very small numbers this way – they take
much less space!
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Weight of a rabbit: 1420 g
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How many significant digits?
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On first inspection, we would say 3 sig dig.
But, maybe the scale measures to the closest
gram and we have 4 significant digits. How can
we be sure? We can’t UNLESS …
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We can take the ambiguity out by using scientific
notation:
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If the value is 1.420 X 103, then we know that the
fourth digit is significant
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For example, the number
65000000 would be
written 6.5 x 107.
In this example the
coefficient equals 6.5
(which meets the
requirement that 1<y<10)
Since there are seven
digits trailing the decimal
between the 6 and 5 we
must move the decimal
point 7 places to the left:
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For example, the number
0.0000987 would be
written 9.87 x 10-5.
In this example the
coefficient equals 9.87
(which meets the
requirement that 1<y<10)
Since there are seven
digits preceding the
decimal between the 9 and
87 we must move the
decimal point 5 places to
the right:
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An electron's mass is about
0.00000000000000000000000000000091093822 kg.
In scientific notation, this is written 9.1093822×10−31 kg.
The Earth's mass is about
5973600000000000000000000 kg.
In scientific notation, this is written 5.9736×1024 kg.
The Earth's circumference is approximately 40000000 m.
In scientific notation, this is 4×107 m.
An inch is 25400 micrometers.
In scientific notation, this is 2.5400×104 µm
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RULE #1: Standard Scientific Notation is a
coefficient (y), with 1 ≤ y < 10 followed by a
decimal and the remaining significant digits
y is multiplied by 10 raised to an exponent
(where the exponent (b) is an integer).
y
x
b
10 :
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y = coefficient or mantissa or significand
b = exponent or power
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where 1 ≤ y < 10 and b = Z (integer)
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Converting a number in these cases means to
either convert the number into scientific
notation form, convert it back into decimal
form or to change the exponent part of the
equation.
None of these changes alter the actual
number, only how it's expressed.
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RULE #2: When the decimal is moved to the left
the exponent gets larger, but the overall value of
the number stays the same. Each place the
decimal moves changes the exponent by one.
When the decimal is moved to the right the
exponent gets smaller,
Example:
= 6000.
= 600.0
= 60.00
= 6.000
6000
x 100
x 101
x 102
x 103
(Note: 100 = 1)
All the previous numbers are equal, but only
6.000 x 103 is in proper Scientific Notation.
 2450000
0.000472
▣ Decimal moves 6 places left
▣ Coefficient becomes 2.45
▣ exponent becomes (+) 6
▣ Decimal moves 4 places right
▣ Coefficient becomes 4.72
▣ exponent becomes -4
 2.45
4.72 x 10-4
1)
2)
3)
x 106
First, move the decimal point to make the
coefficient’s (number's) value between 1 & 10.
If the decimal was moved to the left, increase
the exponent (positive numbers will be
produced).
If the decimal was moved to the right, decrease
the exponent (negative numbers will be
produced).
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4.282 x 104
▣ Decimal moves 6 places left
▣ Coefficient becomes 2.45
▣ exponent becomes (+) 6
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1)
2)
3)
42820
7.5 x 10-5
▣ Decimal moves 4 places right
▣ Coefficient becomes 4.72
▣ exponent becomes -4
0.000075
When converting a number from scientific
notation to decimal notation, first remove the
x 10b on the end
If the exponent (b) is positive, shift the decimal
separator b digits to the right. You will have to
place zeros for unfilled place values. See red
zeros in the example.
If the exponent (b) is negative, shift the decimal
separator b digits to the left. You will have to
place zeros for unfilled place values. See red
zeros in the example.
Convert Decimals to Scientific Notation
1) 72.0
2) 674000
3) 0.000000805
4) 704.02
Convert Scientific Notation to Decimals
1) 3.39 × 10-4
2) 8.05 × 106
3) 2.400 × 105
4) 8.205 × 10-5
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RULE #3: To add/subtract in scientific
notation, the exponents must first be the same.
Example:
(3.0 x 102) + (6.4 x 103); since 6.4 x 103 is
equal to 64. x 102. Now add.
(3.0 x 102)
+ (64. x 102)
67.0 x 102 = 6.70 x 103 = 6.7 x 10
3
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RULE #4: To multiply, find the product of the
numbers, then add the exponents.
Example:
(2.4 x 102) (5.5 x 10 –4) =
[2.4 x 5.5 = 13.2] exponents [2 + -4 = -2]
so
(2.4 x 102) (5.5 x 10 –4) =
13.2 x 10 –2 =
1.3 x 10 – 1
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RULE #5: To divide, find the quotient of the
number and subtract the exponents.
Example:
(3.3 x 10 – 6) / (9.1 x 10 – 8) =
[3.3 / 9.1 = .36]; exponents [-6 – (-8) = 2],
so:
(3.3 x 10 – 6) / (9.1 x 10 – 8) =
.36 x 102 =
3.6 x 10 1
1)
4.90 × 102 + 7.93 × 103
2)
6.95 × 10-4 - 4.89 × 10-5
3)
2.390 × 10-2 + 8.153 × 10-3 + 2.034 × 10-2
4)
1.252 × 106 - 7.08 × 105
1)
(9.2 × 10-6) × (3.0 × 1010)
2)
(3.5 × 106) / (5.0 × 102)
3)
(4.18 × 10-1) × (3.05 × 1010)
4)
(7.15 × 10-6) / (2.735 × 10-4)
5)
(3.0 × 107) × (4.0 × 10-4) / (6.0 × 103)
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Introduction (13:56)
http://www.youtube.com/watch?v=DmeG4rc6NI
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Just watch this one!
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But if you need more help or more practice
watch these Tyler DeWitt Videos (see next
page)
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Practice with Scientific Notation (13:31)
http://www.youtube.com/watch?v=7iGAa0BVS9I
Scientific Notation: Addition & Subtraction (7:12)
http://www.youtube.com/watch?v=PYTp75sryWA
Scientific Notation: Multiplication & Division (5:31)
http://www.youtube.com/watch?v=ciFOlirz4Js
Scientific Notation & Significant Digits (7:58)
http://www.youtube.com/watch?v=IIQPHC5gZT8