Scientific notations
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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 10 6 BP

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Scientific Notations

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Scientific notations

Scientific Notations

Small and Large numbers


Size matters in chemistry

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

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


Examples

Examples

  • 4500 =

  • 305000 =

  • 0.0025 =


Exponents

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


Exponents1

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

Zero exponent

  • Any number raised to zero power is equal to unity

    • 100 =

    • 60 =

    • 1500 =

    • (4 x 103)0 =


Muliplication

Muliplication

  • 102 x 103 x 104 = 102+3+4 =

  • 102x 10-3 x 10-4 = 102+(-3)+(-4) =


Divisions

Divisions

  • 103 / 105=


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