Quantization reduces the numerical precision of large language model weights, trading accuracy for smaller file sizes and lower memory requirements, similar to lossy compression. A 7B parameter model at full FP16 precision requires roughly 14 GB for weights, while consumer GPUs typically have 8 to 24 GB. The comparison covers three levels: Q4_K_M (~4.8 bpw), Q6_K (~6.6 bpw), and Q8_0 (~8.5 bpw). File sizes for a 7B model are ~4.4 GB, ~5.5 GB, and ~7.2 GB respectively. Perplexity loss versus FP16 is +1.5–3% for Q4, +0.5–1.5% for Q6, and +0.1–0.3% for Q8. Q4 is best for general chat and VRAM-constrained setups, Q6 suits code generation and balanced quality/size, and Q8 targets math and precision-critical tasks. Relative speed is fastest for Q4 (15–30% over Q8), middle for Q6, and slowest for Q8, though Q8 remains 1.5–3× faster than FP16. The article presents a decision framework mapping these choices to hardware profiles and use cases, using concrete benchmarks rather than theory.