# How do you convert 8.0 pm/μs to m/s?

Apr 9, 2018

$8.0 p m / \mu s$ should converts to $8.0 \times {10}^{- 6} m / s$ 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 $1 \times {10}^{-} 9$ seconds, and a nano meter is $1 \times {10}^{-} 9$ 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 ($\frac{p m}{\mu s}$) can be represented as such:

$\frac{p m}{\mu s} = \frac{1 \times {10}^{-} 12 m}{1 \times {10}^{-} 6 s} = \frac{1 \times {10}^{-} 12}{1 \times {10}^{-} 6} \frac{m}{s}$

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

$8 \frac{p m}{\mu s} = 8 \times \left(\frac{1 \times {10}^{\cancel{- 12} \textcolor{red}{- 6}}}{1 \times {10}^{\cancel{- 6}}}\right) \frac{m}{s}$

$8 \frac{p m}{\mu s} = 8 \times \left(\frac{1 \times {10}^{-} 6}{1 \times \cancel{{10}^{0}} \textcolor{red}{1}}\right) \frac{m}{s}$

$8 \frac{p m}{\mu s} = 8 \times \left(1 \times {10}^{-} 6\right) \frac{m}{s}$

$8 \frac{p m}{\mu s} = 8 \times {10}^{-} 6 \frac{m}{s}$