Practice Round-off Error (17.1.1.1) - Error Analysis in Numerical ODE Solutions
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Round-off Error

Practice - Round-off Error

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Practice Questions

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Question 1 Easy

What is round-off error?

💡 Hint: Think about how numbers might change when approximated.

Question 2 Easy

Give an example of round-off error.

💡 Hint: What common constant can be rounded?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What causes round-off error?

Finite precision in numbers
Infinite series
Data overflows

💡 Hint: Think about how computers handle numbers.

Question 2

True or False: Round-off errors can accumulate over multiple computations.

True
False

💡 Hint: What's the effect of repetitive approximations?

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Challenge Problems

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Challenge 1 Hard

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.

💡 Hint: Focus on the results of Euler's method and how errors may accumulate.

Challenge 2 Hard

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.

💡 Hint: Try evaluating a mathematical operation using different representations of π.

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