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Scientific Notations
Small and Large numbers
Size matters in Chemistry
 Small sizes:
 Diameter of an atom:
 0.1nm to 0.5 nm
 Concentration of H+ concentrations in pH
 1 x 10-7 M
 Mass of one atom of gold
 3.27 x 10-22 g
 Large numbers:
 DNA molecule – 8.5 cm long with 50 x 106 BP
 A mole = 6.02 x 1023
Why SN
 difficult to write
 difficult to work with, especially in calculations
 To simplify working with these numbers, we use
what is known as scientific notation
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25, 000, 000
Product of two numbers
2.5 x 10,000,000
2.5 x 107
Examples
 4500 =
 305000 =
 0.0025 =
exponents
 A summary of some positive powers of ten are
given below:
 101 = 10
 102 = 100
 103 = 1 000
 104 = 10 000
 105 = 100 000
Exponents
 A summary of some negative powers of ten are
given below:
 10-1 = 1/10 = 0.1
 10-2 = 1/100 = 0.01
 10-3 = 1/1000 = 0.001
 10-4 = 1/10000 = 0.000 1
 10-5 = 1/100000 = 0.000 01
Zero exponent
 Any number raised to zero power is equal to unity
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100 =
60 =
1500 =
(4 x 103)0 =
Muliplication
 102 x 103 x 104 = 102+3+4 =
 102 x 10-3 x 10-4 = 102+(-3)+(-4) =
Divisions
 103 / 105 =