e approximation
The rational approximation 2721/1001 for e is notable because it achieves seven to eight significant figures of accuracy, which is far more precise than the trivial truncation 2718/1000 given its denominator size.
Background
e (Euler's number, ≈ 2.71828) is a fundamental mathematical constant, the base of natural logarithms. John D. Cook is a mathematician and former NASA researcher who writes a popular blog about applied math and computing. The blog post compares rational approximations of e (fractions like 2721/1001) that match e to many decimal places despite having small denominators. The key concept is that any irrational number can be approximated by fractions, but the "accuracy relative to denominator size" (measured by how close the fraction gets vs. how big its denominator is) is a criterion for whether an approximation is genuinely interesting or merely trivial — e.g., truncating the decimal to 2718/1000 is obvious and not very accurate, while 2721/1001 is surprisingly good for its simplicity.