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Scientific Notation
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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 method of representing very
large or very small numbers in
the form:
M x 10n
 M is a number between 1
and 9
 n is an integer equal to the
number of decimal places
moved
.
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 x 10n
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 x 10n
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
Review:
Scientific notation expresses a
number in the form:
M x
1  M  10
n
10
n is an
integer
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
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
Scientific Notation and your
calculator
To enter a number in scientific notation on your
calculator follow these steps:
#1 Type in the decimal number
- ex 6.022
#2 For most TI calculators press 2nd and then the
EE button (usually above the x2 or x-1 buttons)
- This represents x 10n in calculator language
DO NOT TYPE IN x 10^n YOU WILL GET THE
WRONG ANSWER!
List the value of the following
exponential terms
__________ 1) 1.0 x 103
__________ 2) 1.0 x 100
__________ 5) 1.0 x 10-3
Put the following numbers into
scientific notation.
__________ 6) 588.762
__________ 7) 0.00000722
__________ 8) 4,310,000
__________ 9) 0.004100
Take the following numbers out of
scientific notation
____________________ 10)3.67 x 105
____________________ 11)2.099 x 103
____________________ 12)3.1 x 10-1
____________________ 13)5.04 x 10-5
____________________ 14)2.00 x 100
Put the following numbers into
correct scientific notation f sig
figs indicated
________ 15) 30,000 (3 sig figs)
________ 16) 115,000,000 (2 sig figs)
________ 17) 106,000 (4 sig figs)
________ 18) 0.0412 (3 sig figs)
________ 19) 0.0233006 (2 sig figs)
________ 20) 0.00149999999 (3 sig figs)
Solve the following problems. Put the answers into
correct scientific notation form. (Yes, sig figs
matter.)
________ 21) 1.50 x 102 / 2.39 x 10-1
________ 22) 3.29 x 105 / 2.1 x 106
________ 23) 1.50 x 104
*
________ 24) 8.000 x 10-3
________ 25) 2.60 x 106
*
2.3 x 10-3
*
2.67 x 101
1.50 x 10-2