The 260/280 and 260/230 ratios are important in nucleic acid quantification and purity assessment because they indicate the presence of contaminants that can affect the accuracy of the measurements. A high 260/280 ratio suggests the presence of protein contamination, while a low 260/230 ratio indicates the presence of organic contaminants. These ratios help researchers determine the quality and purity of the nucleic acid sample, which is crucial for downstream applications such as PCR and sequencing.