How do you convert 8.0 pm/μs to m/s?

1 Answer
Apr 9, 2018

Answer:

#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#