Scientific Notation

Scientific notation writes any number as

where $N$ is between $1$ and $10$ (exactly one non-zero digit before the decimal point) and $k$ is an integer. It keeps huge and tiny numbers readable.

• Large numbers need a positive $k$ — the decimal point moves right. $4\,500\,000 = 4.5 \times 10^{6}$.
• Small numbers need a negative $k$ — the decimal point moves left. $0.00032 = 3.2 \times 10^{-4}$.

The exponent $k$ is simply how many places the decimal point moves to turn $N$ back into the ordinary number. South Africa's population is roughly $6 \times 10^{7}$ (60 million) — far easier to read than a string of zeros.