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  "body": "\n## Statement\n\nLet $x$ be a real number with $x \\ge 0$.\nThen $x$ has a [[decimal expansion|06XY4X9430]]: there are a natural number $a_0$ and digits $d_k \\in \\{0, \\dots, 9\\}$ for $k \\ge 1$ with $x = a_0 + \\sum_{k=1}^{\\infty} d_k 10^{-k}$.\n\n## Remarks\n\nOne choice is $a_0 = \\lfloor x \\rfloor$ and $d_k = \\lfloor 10^k x \\rfloor - 10 \\lfloor 10^{k-1} x \\rfloor$, with the [[floor function|0YVRNEDSVG]].\nWith this choice, the truncation $a_0.d_1 \\dots d_k$ satisfies $0 \\le x - a_0.d_1 \\dots d_k \u003c 10^{-k}$.\nThe expansion is unique, except for the numbers with a finite expansion. They also have a second expansion that ends in infinitely many $9$.\n\n## Explanations\n\n### L1 human\n\nYou can find the digits of a number one at a time.\nAt each step, you choose the largest digit that keeps the truncated decimal at or below the number.\nThe truncations then get closer to the number by a factor of ten at each step.\n",
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