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I have two layers in QGIS, one the coordinate system of WGS84 and another uses GRS80. The two layers overlap, which looks good. My question is do I have to reproject them to the same coordinate system or just leave them as they are? Someone told me that reprojection could introduce inaccuracies to the data. So does it matter if I don't reproject? Under what situations is the reprojection needed?

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    Welcome to GIS SE. As a new user, please take the Tour. Two geographic CS will always overlap, even without datum transformation, because they share the same angular measurement domain (2pi x pi). If the data registers well, it's because "on-the-fly reprojection" is doing transformation. If the data doesn't register well, then datum transformation is not occurring (or the data is just of poor quality -- that happens, too). Either way, static reprojection is only necessary if you want to end the computation cost of dynamic reprojection. – Vince Feb 24 at 14:23
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They are reprojected on the fly to your projects coordinate system.

As long as you won't do any geoprocessing with them, there is no need to reproject your layers.

Also see: https://docs.qgis.org/2.8/en/docs/user_manual/working_with_projections/working_with_projections.html

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