Question

How do you convert 8.0 pm/μs to m/s?

Answer 1

`8.0 p m//mu s` should converts to `8.0xx10^(-6) m//s` using SI unit conversion.

Explanation:

The lovely thing about SI units is that all of the prefixes mean the same thing, and have numeric equivalents. For example, a nano second is `1xx10^-9` seconds, and a nano meter is `1xx10^-9` meters.

For the requested conversion, we have picometers (`p m`) and microseconds (`mu s`).

The "pico" prefix is equivalent to `10^-12` of the base unit.
The "micro" prefix is equivalent to `10^-6` of the base unit.

So, a picometer per microsecond (`(p m)/(mu s)`) can be represented as such:

`(p m)/(mu s)=(1xx10^-12 m)/(1xx10^-6 s)=(1xx10^-12)/(1xx10^-6) m/s`

Now that we have our numeric representation, we can reduce the fraction and get a conversion constant, ultimately giving us our answer:

`8(p m)/(mu s)=8xx((1xx10^(cancel(-12)color(red)(-6)))/(1xx10^(cancel(-6)))) m/s`

`8(p m)/(mu s)=8xx((1xx10^-6)/(1xxcancel(10^(0))color(red)(1))) m/s`

`8(p m)/(mu s)=8xx(1xx10^-6)m/s`

`8(p m)/(mu s)=8xx10^-6m/s`