In this paper, a simple technique for encoding fractional bit components used in fixed-rate Gaussian mixture model-based (GMM) block quantisers is presented. While block transform image coding has not been very popular lately in the presence of current state-of-the-art wavelet-based coders, the GMM-based block quantiser, without the use of entropy coding, is still very competitive in the class of fixed-rate transform coders. It consists of a set of individual block quantisers operating at different bitrates, and the problem is that these bitrates are mostly fractional. Fixed-rate block quantisers based on an integer number of bits can be designed and through the use of heuristic algorithms, can approach the fractional target rate. However, the use of level-based scalar quantisers in the block quantiser allows better utilisation of the bit budget; a finer `spread' of the bit budget across components; and better preservation of optimality. Our technique, which is based on a generalisation of positional value number systems, allows the use of level-based scalar quantisers in a fixed-rate coding framework. Experimental results comparing the use of the bits-based GMM-based block quantiser with the levels-based one in image coding show a finite improvement in the PSNR performance.