Question

Convert the speed of light (3.0 x 10^8m/s) from meters per second (m/s) to nanometers per picosecond (nm/ps)

Answer 1

In 1 meter, there are $10^9$ nanometers, and in 1 second there are $10^{12}$ picoseconds, so we have

$\dfrac{3.0\times10^8\text{ m}}{1\text{ s}}\cdot\dfrac{10^9\text{ nm}}{1\text{ m}}\cdot\dfrac{1\text{ s}}{10^{12}\text{ ps}}=3.0\times10^{8+9-12}=3.0\times10^5\dfrac{\text{nm}}{\text{ps}}$