In the Imperial Radch trilogy of novels, the protagonist Breq Mianaai is in possession of a powerful weapon created by the alien Presger. The weapon is a relic from the failed resistance of Garsedd (which acquired the weapon from the Presger) to annexation by the Radch.
It is established that bullets fired from the weapon will, upon contact with any object, penetrate that object to a distance of 1.11 metres (and no further).
In Ancillary Mercy, Breq (and the audience) learns that the distance of 1.11 metres is not intentional, and is instead a side-effect of its design. As Presger Translator Zeiat explains:
"It wasn't meant to be a useful distance. In fact, the distance wasn't meant at all...the bullets aren't designed to go through anything for 1.11 meters. They're designed to destroy Radchaai ships. That was what the purchasers required of them. The 1.11 meters is a kind of... accidental side effect sort of thing. And useful in its own way of course." (Ancillary Mercy, Chapter 9)
This provides an in-universe answer to the significance of the 1.11m, however, is there an out of universe explanation as to why the ammunition of the Presger gun is limited to this distance? Is there any significance to this detail being 1.11 metres?
Comments from the author on the subject, or theories with explanation, are both acceptable and encouraged.