John D. Cook • 6/27/2026

When will the decimals in a/b repeat?

This article investigates the repeating decimal patterns in fractions derived from harmonic numbers. It provides Python code using SymPy to compute the period length of the decimal expansion of 1/lcm(1..n), determining both non-repeating and repeating digit segments. The example shows that for n=50, there are 5 non-repeating digits followed by 1,275,120 repeating digits. The content is technical, focusing on number theory, algorithms, and programming, making it relevant to IT/technology.

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#Python #Sympy #Harmonic Numbers