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Scientific Notations

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 10 6 BP

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Scientific Notations

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  1. Scientific Notations Small and Large numbers

  2. 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

  3. 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 • 25, 000, 000 • Product of two numbers • 2.5 x 10,000,000 • 2.5 x 107

  4. Examples • 4500 = • 305000 = • 0.0025 =

  5. 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

  6. 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

  7. Zero exponent • Any number raised to zero power is equal to unity • 100 = • 60 = • 1500 = • (4 x 103)0 =

  8. Muliplication • 102 x 103 x 104 = 102+3+4 = • 102x 10-3 x 10-4 = 102+(-3)+(-4) =

  9. Divisions • 103 / 105=

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