Download Sci. Notation - Standard Form

STANDARD FORM
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


9,200,000,000,000,000
.0000000000254
-23,000,000,000
-.000091
SCIENTIFIC
NOTATION
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9.2 x 1015
2.54 x 10-11
-2.3 x 1010
-9.1 x 10-5
1. An ordinary quarter contains about
97,700,000,000,000,000,000,000 atoms.
2. The average size of an atom is about 0.00000003
centimeters across.
These very long numbers are written in **STANDARD
FORM**
**The length of these numbers in standard
notation makes them awkward to work
with.
Scientific notation is a shorthand way of
writing numbers – instead of standard
notation.
82,000,000
1.
Find a number bigger
than 1, less than 10
a.
b.
2.
Only 2 decimal places
This is your NEW
decimal
1.
8.2
2.
8.2 x 10
3.
7 Spaces (8.2 x 107)
4.
LEFT
Multiply by 10 ( x 10)
3. Count decimal spaces
from NEW to OLD (this
is your exponent on 10)
4. LEFT = POSITIVE
RIGHT = NEGATIVE
(exponent)
In scientific notation the number of atoms in
a quarter (97,700,000,000,000,000,000,000 ) is
9.77  1022
and the size of each atom (0.00000003)
is
3.0  10–8 centimeters across.
Example
2:
Write 0.00709 in scientific notation.
0.00709
Move the decimal to get a number between 1 and 10.
7.09  10
(*you want only one number behind the
decimal)
Set up in scientific notation.
Think: The decimal needs to move left to change 7.09
to 0.00709, so the exponent will be negative.
Think: The decimal needs to move 3 places
So 0.00709 written in scientific notation is 7.09 
10–3Check
.
7.09  10–3 = 7.09  0.001 = 0.00709
Example
3:A pencil is 18.7 cm long. If you were to lay 10,000
pencils end-to-end, how many millimeters long
would they be? Write the answer in scientific
Hint:
notation.
1. Convert from cm to mm
2. Find the length of 10,000
pencils
1 cm = 10 mm
18.7 cm = 187 mm
187 mm  10,000
1,870,000 mm
KHDMDC
M
Multiply each side by
10 Find the total
length.
Multipl
y
Example 3
continued:
1.87  106
Set up scientific notation.
Think: The decimal needs to move right
to change 1.87 to 1,870,000, so the exponent will
be positive.
Think: The decimal needs to move 6 places.
In scientific notation the 10,000 pencils would be 1.87  106 mm
long, laid end-to-end.
(5.23 X 107)



The exponent on the 10 tells you how many spaces
you will move the decimal
If the exponent is POSITIVE
move RIGHT
If the exponent is NEGATIVE
move LEFT
EXAMPLES:
3.75 x 109 = 3,750,000,000
8.62 x 10-6 = .00000862
Example
1:
Write the number in standard notation:
A. 1.35  105
BECAUSE
1.35  105
1.35  100,000
135,000
105 = 100,000
Think: Move the decimal right 5
places.
Helpful Hint
A positive exponent means move the decimal to the right,
and a negative exponent means move the decimal to the
Example Write the number in standard notation:
1:
HINT:
–3
B. 2.7  10
Just remember that since the
exponent is negative we move
the decimal to the left 3 spaces
2.7  10–3
1
2.7  10x10x10
10 -3
2.7  1000
0.0027
1
= 1000
Divid by the reciprocal.
e
Think: Move the decimal left 3 places.
Example Write the number in standard notation:
1:
C. -2.01 
HINT:
It doesn’t matter that the number (104
-2.01  104
2.01) is negative – only the exponent
changes things
-2.01 
104 = 10,000
-20,100
10,000
Think: Move the decimal right 4
places.
**Because 4 is
POSITIVE**
Quiz:
Write each number in standard notation.
1. 1.72  104
17,200
2. 6.9  10–3
0.0069
Write each number in scientific notation.
3. 0.0053
5.3  10–3
4. 57,000,000
5.7  107
5. Order the numbers from least to greatest:
2  10–4 , 9  10–5 , 7  10–5
7  10–5, 9  10–5, 2  10–4