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Scientific Notations

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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

- Diameter of an atom:
- 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=