Aboard an orbiting research station, Emek and Luna received four navigation signals: 7/8, 1.25, sqrt(36), and sqrt(11). Before the station could adjust its orbit, each value had to be sent through either the rational or irrational channel. Emek identified 7/8 as rational because it was a ratio of integers. Luna noted that 1.25 was also rational because the terminating decimal could be written as 5/4. Although sqrt(36) contained a square root symbol, they simplified it to 6, so it belonged in the rational channel too. The final value, sqrt(11), could not be simplified to an integer or written as a ratio of integers, so they classified it as irrational. Luna checked that three signals were rational and one was irrational before confirming the routing. With every value sent through the correct channel, the guidance system accepted the data and safely moved the station into its new orbit.