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Understanding Scientific Notation: Simplifying Small and Large Numbers in Chemistry

Scientific notation is essential in chemistry for managing the extraordinarily small and large numbers that often arise. For instance, an atom's diameter ranges from 0.1 nm to 0.5 nm, while a mole contains approximately 6.02 x 10²³ particles. This notation simplifies operations, such as multiplication and division of large quantities by converting them into a more manageable form. Key examples include the mass of a single gold atom (3.27 x 10⁻²² g) and concentrations represented in pH (1 x 10⁻⁷ M). Learning scientific notation is crucial for calculation efficiency.

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Understanding Scientific Notation: Simplifying Small and Large Numbers in Chemistry

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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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