Light travels $3\times 10^8$ m in one second. How far does it travel in $2\times 10^{-3}$ second?

Multiply the decimal parts and add the powers: $\left(3\times 2\right)\times 10^{8+(-3)}=6\times 10^5$ m. Multiplying the exponents gives $10^{-24}$, treating the $-3$ as $+3$ gives $10^{11}$, and adding $3+2$ instead of multiplying gives 5.