1. Scientific Notations Small and Large numbers

2. Size matters in Chemistry Small sizes: Small sizes: Diameter of an atom: Diameter of an atom: 0.1nm to 0.5 nm 0.1nm to 0.5 nm Concentration of H + concentrations in pH Concentration of H + concentrations in pH 1 x 10 -7 M 1 x 10 -7 M Mass of one atom of gold Mass of one atom of gold 3.27 x 10 -22 g 3.27 x 10 -22 g Large numbers: Large numbers: DNA molecule – 8.5 cm long with 50 x 10 6 BP DNA molecule – 8.5 cm long with 50 x 10 6 BP A mole = 6.02 x 10 23 A mole = 6.02 x 10 23

3. Why SN difficult to write difficult to write difficult to work with, especially in calculations difficult to work with, especially in calculations To simplify working with these numbers, we use what is known as scientific notation To simplify working with these numbers, we use what is known as scientific notation 25, 000, 000 25, 000, 000 Product of two numbers Product of two numbers 2.5 x 10,000,000 2.5 x 10,000,000 2.5 x 10 7 2.5 x 10 7

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

5. exponents A summary of some positive powers of ten are given below: A summary of some positive powers of ten are given below: 10 1 = 10 10 1 = 10 10 2 = 100 10 2 = 100 10 3 = 1 000 10 3 = 1 000 10 4 = 10 000 10 4 = 10 000 10 5 = 100 000 10 5 = 100 000

6. Exponents A summary of some negative powers of ten are given below: A summary of some negative powers of ten are given below: 10 -1 = 1/10 = 0.1 10 -1 = 1/10 = 0.1 10 -2 = 1/100 = 0.01 10 -2 = 1/100 = 0.01 10 -3 = 1/1000 = 0.001 10 -3 = 1/1000 = 0.001 10 -4 = 1/10000 = 0.000 1 10 -4 = 1/10000 = 0.000 1 10 -5 = 1/100000 = 0.000 01 10 -5 = 1/100000 = 0.000 01

7. Zero exponent Any number raised to zero power is equal to unity Any number raised to zero power is equal to unity 10 0 = 10 0 = 6 0 = 6 0 = 150 0 = 150 0 = (4 x 10 3 ) 0 = (4 x 10 3 ) 0 =

8. Muliplication 10 2 x 10 3 x 10 4 = 10 2+3+4 = 10 2 x 10 3 x 10 4 = 10 2+3+4 = 10 2 x 10 -3 x 10 -4 = 10 2+(-3)+(-4) = 10 2 x 10 -3 x 10 -4 = 10 2+(-3)+(-4) =

9. Divisions 10 3 / 10 5 = 10 3 / 10 5 =