Advanced Topic 41 of 51 Math for Computing
Floating Point Error
Rounding and precision limits in machine arithmetic.
How it works
Rounding error, catastrophic cancellation (subtracting nearly equal numbers) and absorption (adding tiny to huge values) limit accuracy; machine epsilon ≈ 2.2×10⁻¹⁶ for doubles. Use Kahan summation and compare with tolerances.
Where it is used
Numerical code.
Common pitfall
Never test floats for exact equality.
Where it fits in the course
Floating Point Error is topic 41 of 51 in Math for Computing, rated Advanced. It follows Numerical Methods. The next topic is Root Finding.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Math for Computing quiz.
- Explore the Binary & Two's Complement visualizer: Flip bits and watch the number change.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Math for Computing quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Floating Point Error?
Rounding and precision limits in machine arithmetic. It belongs to Math for Computing and is an advanced-level topic.
Where do people use Floating Point Error?
Numerical code.
What is the most common mistake with Floating Point Error?
Never test floats for exact equality.
What should I learn before this topic?
Start with Numerical Methods, the topic just before it in Math for Computing.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Math for Computing quiz. You can also explore Binary & Two's Complement in the Visual Lab.
Is Floating Point Error hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn Floating Point Error?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Floating Point Error?
Numerical Methods, Root Finding, Simplex Method are closely connected. The full list is in the related topics section of this page.
What should I study after Floating Point Error?
Continue with Root Finding, the next topic in Math for Computing.
Related topics
- Numerical Methods (Math for Computing)
- Root Finding (Math for Computing)
- Simplex Method (Math for Computing)
- Numerical Integration (Math for Computing)
- Floating Point Representation (Computer Architecture & Logic)
- Error Detection and Correction (Computer Networks)
- Error Handling (Programming Fundamentals)