Chemistry involves the study of atoms and molecules,which have extremely low masses and are present in extremely large numbers.
Chemists often deal with very large numbers,such as $602,200,000,000,000,000,000,000$ for the number of molecules in $2 \ g$ of hydrogen gas,or very small numbers,such as $0.00000000000000000000000166 \ g$ for the mass of a single $H$ atom.
To simplify calculations,scientific notation (exponential notation) is used,where any number is represented as $N \times 10^{n}$.
Here,$n$ is an exponent that can be positive or negative,and $N$ is a digit term varying between $1.000$ and $9.999$.
For example,$232.508$ is written as $2.32508 \times 10^{2}$,and $0.00016$ is written as $1.6 \times 10^{-4}$.
Multiplication and Division:
These operations follow standard rules for exponents.
Example (Multiplication): $(5.6 \times 10^{5}) \times (6.9 \times 10^{8}) = (5.6 \times 6.9) \times 10^{5+8} = 38.64 \times 10^{13} = 3.864 \times 10^{14}$.
Example (Division): $\frac{2.7 \times 10^{-3}}{5.5 \times 10^{-4}} = (2.7 \div 5.5) \times 10^{-3 - (-4)} = 0.4909 \times 10^{1} = 4.909$.
Addition and Subtraction:
For these operations,the numbers must first be converted to have the same exponent.
Example (Addition): $6.65 \times 10^{4} + 8.95 \times 10^{3} = 6.65 \times 10^{4} + 0.895 \times 10^{4} = (6.65 + 0.895) \times 10^{4} = 7.545 \times 10^{4}$.
Example (Subtraction): $2.5 \times 10^{-2} - 4.8 \times 10^{-3} = 2.5 \times 10^{-2} - 0.48 \times 10^{-2} = (2.5 - 0.48) \times 10^{-2} = 2.02 \times 10^{-2}$.