Digital computation is central to almost all scientific endeavors and has become integral to university physics education. Students collect experimental data using digital devices, process data using spreadsheets and graphical software, and develop scientific programming skills for modeling, simulation, and computational work. Issues associated with the floating-point representation of numbers are rarely explored. In this article, problems of floating point are divided into three categories: significant-figure limits, propagation of floating-point representation error, and rounding. For each category, examples are presented of unexpected ways, in which the digital representation of floating-point numbers can impact the veracity of scientific results. These examples cover aspects of classical dynamics, numerical integration, cellular automata, statistical analysis, and digital timing. Suggestions are made for curriculum enhancement and project-style investigations that reinforce the issues covered at a level suitable for physics undergraduate students.

中文翻译：

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浮点数：意想不到的故事

数字计算几乎是所有科学工作的核心，并已成为大学物理教育不可或缺的一部分。学生使用数字设备收集实验数据，使用电子表格和图形软件处理数据，并培养建模、模拟和计算工作的科学编程技能。很少探讨与数字的浮点表示相关的问题。在本文中，浮点问题分为三类：有效数字限制、浮点表示错误的传播和舍入。对于每个类别，示例都以意想不到的方式呈现，其中浮点数的数字表示会影响科学结果的准确性。这些例子涵盖了经典动力学、数值积分、元胞自动机、统计分析和数字计时。对课程改进和项目式调查提出了建议，以在适合物理本科生的水平上加强所涵盖的问题。