In parallel dimension #1729, CALVIN National Laboratories has discovered a new unstable sub-atomic particle, the Biggs Hoson, which resulted from a high-energy collision between two stable sub-atomic particles in a collision chamber similar to the one at CERN (pictured below).

Thanks to parallel dimensions #1729's awesome technology, they were able to trace the path of the Biggs Hoson after it was born and found that the arc length of its trajectory was exactly \(1\) meter before decaying, and that its lifespan at rest was exactly \(10^{-9}\) seconds.

If \(v_{0}\) is the average speed of the Biggs Hoson after the collision, what is the value of \(\dfrac{v_{0}}{c}\) rounded to 3 decimal places?

**Details and Assumptions:**

- \(c\) is the speed of light, which also happens to be \(\si{3\times10^8} \si[per-mode=symbol]{\metre\per\second} \) in parallel dimension #1729.
- Light speed is still the universal speed limit. Nothing can travel faster than a photon, and it always travels at \(c\) relative to any intertial observer.

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