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2 cards from this section. Quick, good the night before a test.
What is round-off error?
Think about how numbers might change when approximated.
Give an example of round-off error.
What common constant can be rounded?
What causes round-off error?
Think about how computers handle numbers.
True or False: Round-off errors can accumulate over multiple computations.
What's the effect of repetitive approximations?
Consider a simple numerical integration using Euler's method with a step size of h = 0.1. If the initial value is x = 1, compute the next value after one iteration. Now assume rounding to the nearest hundredth at each step. Analyze how the result is affected by round-off error.
Focus on the results of Euler's method and how errors may accumulate.
If you take π and represent it with three different levels of precision (1 decimal, 2 decimals, and 5 decimals), how do you expect the accuracy of numerical computations to change? Illustrate how using more digits would minimize round-off error.
Try evaluating a mathematical operation using different representations of π.
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