A week was small number days grouped together as part of a calendar system. On Earth a week was seven days.
The colony ship SS Conestoga transmitted weekly status reports during the Terra Nova Expedition. These reports were reviewed by Ensign Travis Mayweather in 2151. (ENT: "Terra Nova")
On June 19th 2151, Sub-commander T'Pol was aboard Enterprise NX-01 for nine weeks and four days. (ENT: "The Andorian Incident")
In August of 2151, Enterprise was sent to assist the Earth Cargo Service freighter ECS Fortunate as the nearest Starfleet vessel would need three weeks to arrive but Enterprise would only need one day and a half at maximum warp. (ENT: "Fortunate Son")
Takret only needed to sleep once a week. (ENT: "The Catwalk")
Travis Mayweather and his father once took shelter in the ship's core to protect against a class 3 neutronic storm. They were there for six weeks. (ENT: "The Catwalk")
Romulans also groped their days into weeks. On the third day of the Romulan week the Romulan Senate was not in session. (TNG: "Unification I")
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