Download Coefficient x 10(exponent) - Hicksville Public Schools

9/9/2015
The Problem With The Very Big and The Very Small
Believe It Or Not...
...scientific notation makes things easier.
It’s just a standardized way of writing very
bi and
big
d very smallll numbers.
b
Unit 1: Science Is A Verb!
Lesson 1.4: Scientific Notation
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Chemistry Deals With Really Big and Really Small
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Scientific Notation Always Looks Like This:
Examples:
(exponent)
Coefficient x 10
There are ~
Coefficient- ALWAYS larger than or equal to 1
but smaller than 10
160,000,000,000,000,000,000,000 atoms of
carbon in a typical pencil.
A typical carbon atom is ~0.00000000015 meters
in diameter.
exponent- how many powers of 10 you would
need to multiply or divide the coefficient by to
get back to the unscientifically notated
version of the number
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Big Numbers
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Big Examples: Back and Forth
For numbers larger than 1, the exponent will
ALWAYS be a positive number.
The Earth is 4 600 000 000 years old. This number in scientific notation is: 4.6 x109
1) The coefficient is 4.6
2) After the 4, there are 9 places back to the “ones” place = exponent f
h
h
9 l
b k
h “
” l
of X 109
There are 33 400 000 000 000 000 000 molecules in one milliliter of water. This number in scientific notation is: 3.34 x1019
1) The coefficient is 3.34
2) After the first 3, there are 19 places back to the “ones” place = exponent of X 1019
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Small Numbers
Small Examples: Back and Forth
For numbers smaller than 1, the exponent will
ALWAYS be a negative number.
An atom of carbon weighs 0.000 000 000 000 000 000 000 1993 g. This number in scientific notation is: 1.993 x10‐22
1) The first integer in the coefficient is 1, followed by a decimal point, followed by the rest of the digits = 1.993
2)) There are 22 places in front of the first integer = exponent of p
g
p
X 10‐22
The distance between H atoms in a molecule of H2 gas is 0.000 000 0370 mm. This number in scientific notation is: 3.70 x10‐8
1) The first integer in the coefficient is 3, followed by a decimal point, followed by the rest of the digits = 3.70
2) There are 8 places in front of the first integer back to the ones place = exponent of X 10‐8
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But Wait! That’s Not All!
Practice
Exponents let us do some interesting things
with math:
1. Circle the larger value in the pairs below:
a) 2.0 x 105 or 3.0 x 104
b) 5.7 x 10
5 7 x 1012 or 1.3 x 10
or 1 3 x 107
c) 3.3 x 10‐6 or 9.7 x 10‐2
d) 6.5 x 10‐2 or 2.8 x 100
Multiplying
p y g exponents
p
=
Add them!
Dividing exponents =
Subtract them!
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Multiplication and Division
(always, always, always)
Let’s try two!
Multiply 1.25 x 1016 by 4.00 x 1030
1. Do the math that involves your
coefficients first
•
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This includes significant figure rounding, of
course
2. Then deal with the exponential
calculations
Divide 6.25 x 104 by 1.25 x 1010
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Addition and Subtraction
(always, always always)
Let’s Try Two More!
Add 4.02 x 1010 + 9.23 x 109
1. Adjust the exponents first.
2. Then do the math that involves the
(adjusted) coefficients.
• This includes significant figure
rounding, of course (more on this in our
next lesson).
Subtract 1.4 x 105 from 8.2 x 104
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Scientific Notation and your Calculator
Calculator Tip
Most calculators have a short‐cut to deal with Powers of 10 exponents. This is usually signified with a button that says “E” or “EE”.
If you’re feeling saucy, you can write scientific notation this way in general:
Ex.
1.356 x 1037 = 1.356 E37
The scientific notation key
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Scientific Notation and your Calculator
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