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The "scale" and "scale ratio" in terms of railway modelling provides information about the size of the given model train track system and rolling stock relative to the real tracks and real trains moving on them. When talking for model trains, each scale has a name and ratio i.e. HO (1/87). It means that model tracks and trains in HO scale are 87 times smaller than the real ones.
Sometimes, "scale" is confused with "gauge" and vice versa. As stated above, "scale" is the ratio between a unit of measurement on a model train compared to the unit of measurement in corresponding full size prototype, while "gauge" is the distance between the inner edges of the two rails of the model railroad track.
See alsoRail transport modelling scales in Wikipedia