Precision errors often arise from floating-point arithmetic. To avoid them, use integer arithmetic or libraries that support arbitrary precision for critical calculations.

Precision errors are a common issue in competitive programming, especially when dealing with floating-point arithmetic. Computers represent floating-point numbers with a finite precision, which can lead to small rounding errors that accumulate over multiple operations. These errors can cause incorrect results, especially in problems that require high accuracy or involve very small or very large numbers. One way to deal with precision errors is to avoid floating-point arithmetic whenever possible and use integer arithmetic instead. For example, in problems involving fractions, you can represent numbers as ratios of two integers and perform all operations using integer arithmetic. Another option is to use programming languages or libraries that support arbitrary precision arithmetic, such as Python’s decimal module or Java’s BigDecimal class, which allow you to perform calculations with as much precision as needed. In some cases, problems can be designed to avoid precision issues by multiplying values by a constant (such as 100 or 1000) to work with integers instead of decimals. It's also important to be aware of the limits of floating-point precision when comparing numbers. Instead of checking if two floating-point numbers are exactly equal, use a small tolerance value (epsilon) to determine if they are close enough to be considered equal. Understanding how to handle precision errors is essential for solving problems that involve mathematical computations, geometry, or physics simulations in competitive programming.