Transcript Law v. Theory

Scientific
Notation
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
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Scientific Notation:
A. This is essentially a way of writing numbers
with large amounts of digits in a condensed
form.
B. Only significant figures are written when
using Scientific Notation.
C. It is also based on the powers of 10; but
as exponents.
• Exponents are whole numbers written in
superscript to represent a specific number of
places the decimal point has moved.
Scientific Notation:
• Exponents are whole numbers written in
superscript to represent a specific
number of places the decimal point has
moved.
• If the exponent is a positive whole number,
the decimal point has been moved to the
left.
• This would be a larger than 1 number.
• If the exponent is a negative whole
number, the decimal point has been moved
to the right.
• This would be a smaller than 1 number.
Scientific Notation:
D. Numbers written in scientific notation have a
basic format:
M.N X 10Z
• M = First Significant digit in the number
(always followed by the decimal point)
• N = Second Significant digit in the number,
there could be more than 2 sig figs
• Z = a whole number representing the
number of places the decimal point has
moved.
For example:
1,000,000.0 g = 1.0 X 106 g
250.0 L = 2.5 X 102
0.000465 m = 4.65 X 10-4 m
.
2 500 000 000
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M.N x 10z
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M.N x 10z
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
E. ADDITION AND SUBTRACTION
4 x 106
6
+ 3 x 10
7 x 106
IF the exponents are
the same, we simply
add or subtract the
numbers in front and
bring the exponent
down unchanged.
106
6
10
4 x
- 3 x
1 x 106
The same holds true
for subtraction in
scientific notation.
106
4 x
+ 3 x 105
If the exponents are
NOT the same, we
must move a decimal
to make them the
same.
6
10
4.00 x
4.00 x
6
5
+ .30 x 10
+ 3.00 x 10
6
4.30 x 10
Move the
decimal on
the smaller
number!
6
10
A Problem for you…
-6
10
2.37 x
-4
+ 3.48 x 10
Solution…
-6
002.37
2.37 x 10
-4
+ 3.48 x 10
Solution…
-4
0.0237 x 10
-4
+ 3.48
x 10
-4
3.5037 x 10
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
MULTIPLICATION AND DIVISION
F. MULTIPLICATION
Multiplication using Scientific Notation:
1.The significant digits, of each number,
are multiplied first.
2.Then the exponents are added
together.
For example:
(2.4 X 105) • (3.6 X 103) = 8.64 X 108
G. DIVISION
Division using Scientific Notation:
1.The significant digits are divided
first.
2.Then the exponents are
subtracted.
For example:
2.45 X 1023 = 0.43 X 1011
5.65 X 1012
= 4.3 X 1010