Scientific notation

Scientific notation is a method of writing a number as the product of a number greater than or equal to 1 but less than 10 and a power of 10. For example, $412.36$ becomes $4.1236 \times 10^2$.

Multiply by handling numbers and powers separately: $(3 \times 10^4)(2 \times 10^2) = (3 \cdot 2) \times 10^{4+2} = 6 \times 10^6$. Divide in the same way: $\frac{8 \times 10^9}{4 \times 10^3} = (\frac{8}{4}) \times 10^{9 3} = 2 \times 10^6$. A large number: $5,400,000 = 5.4 \times 10^6$.

Tired of writing tons of zeros for huge or tiny numbers? Scientific notation keeps numbers tidy by using powers of 10 to show how many places the decimal point has moved. It's the universe's shorthand.