Final answer:
Scientists are confident in detecting gravitational waves because of the precision of instruments like LIGO, which can detect extremely small length changes. Confirmation from multiple detectors and indirect evidence from astronomical observations assures the reliability of these measurements.
Step-by-step explanation:
Scientists have confidence in detecting gravitational wave signals despite the extremely small length changes because of highly sensitive and precise instruments, such as those used by the Laser Interferometer Gravitational-Wave Observatory (LIGO). LIGO operates with two detectors located far apart to simultaneously measure movements caused by gravitational waves, ensuring that any detected signal isn't a local anomaly, like a minor earthquake or normal traffic. To accomplish this, LIGO's instruments must measure changes as minute as one ten-thousandth the diameter of a proton. This level of precision coupled with the replication of results in both detectors provides strong evidence for the detection of gravitational waves.
Moreover, previous indirect observations and theoretical calculations have supported the existence of gravitational waves. The detection of changes in the orbit of a binary neutron star system by Joseph Taylor and Russell Hulse, conforming precisely to predictions made by general relativity, provided strong indications even before direct detection was possible. The LIGO system further incorporates coincidental detection with astrophysical events, increasing the reliability of a true gravitational wave detection. With these methods and confirmations from multiple locations and circumstances, scientists can be confident in their measurements of these exceptionally small length changes.