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The purpose of this paper is to put the description of number scaling and itseffects on physics and geometry on a firmer foundation, and to make it moreunderstandable. A main point is that two different concepts, number and numbervalue are combined in the usual representations of number structures. This isvalid as long as just one structure of each number type is being considered. Itis not valid when different structures of each number type are beingconsidered. Elements of base sets of number structures, considered bythemselves, have no meaning. They acquire meaning or value as elements of anumber structure. Fiber bundles over a space or space time manifold, M, aredescribed. The fiber consists of a collection of many real or complex numberstructures and vector space structures. The structures are parameterized by areal or complex scaling factor, s. A vector space at a fiber level, s, has, asscalars, real or complex number structures at the same level. Connections aredescribed that relate scalar and vector space structures at both neighbor Mlocations and at neighbor scaling levels. Scalar and vector structure valuedfields are described and covariant derivatives of these fields are obtained.Two complex vector fields, each with one real and one imaginary field, appear,with one complex field associated with positions in $M$ and the other withposition dependent scaling factors. A derivation of the covariant derivativefor scalar and vector valued fields gives the same vector fields. Thederivation shows that the complex vector field associated with scaling fiberlevels is the gradient of a complex scalar field. Use of these results in gaugetheory shows that the imaginary part of the vector field associated with Mpositions acts like the electromagnetic field. The physical relevance of theother three fields, if any, is not known.

Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory