We developed a technology for detecting and quantifying trace nucleic acids using a bracketing protocol designed to yield a copy number with approximately ± 20% accuracy across all concentrations. The microRNAs (miRNAs) let-7b, miR-15b, miR-21, miR-375 and miR-141 were measured in serum and urine samples from healthy subjects and patients with breast, prostate, or pancreatic cancer. Detection and quantification were amplification-free and enabled using osmium-tagged probes and MinION, a nanopore array detection device. Combined serum from healthy men (Sigma‒Aldrich #H6914) was used as a reference. Total RNA isolated from biospecimens using commercial kits was used as the miRNA source. The unprecedented ± 20% accuracy led to the conclusion that miRNA copy numbers must be normalized to the same RNA content, which in turn illustrates (i) independence from age, sex, and ethnicity, as well as (ii) equivalence between serum and urine. miR-21, miR-375 and miR-141 copies in cancers were 1.8-fold overexpressed, exhibited zero overlap with healthy samples and had a p value of 1.6x10-22, tentatively validating each miRNA as a cancer biomarker. miR-15b was confirmed to be cancer-independent, whereas let-7b appeared to be a cancer biomarker for prostate and breast cancer, but not for pancreatic cancer.