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# Scientific Notations - PowerPoint PPT Presentation

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

Small and Large numbers

• 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

• 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

• 4500 =

• 305000 =

• 0.0025 =

• A summary of some positive powers of ten are given below:

• 101 = 10

• 102 = 100

• 103 = 1 000

• 104 = 10 000

• 105 = 100 000

• 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

• Any number raised to zero power is equal to unity

• 100 =

• 60 =

• 1500 =

• (4 x 103)0 =

• 102 x 103 x 104 = 102+3+4 =

• 102x 10-3 x 10-4 = 102+(-3)+(-4) =

• 103 / 105=