Sampling Theorem: How to know the value between two samples of a Signal
Interpolation using a Sinc function kernel.  This assumes that the sampled signal was perfectly bandlimited to below half the sampling rate.

Note that perfectly bandlimited signal are infinite in extent.  For finite-length "real world" signals, using a windowed Sinc interpolation kernel (thus a finite computation with a noise floor) is a common method to approximate points between samples (for upsampling, for instance).