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Number Representation and Floating Point

Truncation, rounding and accuracy

  • 3 things to know
  • A2 Unit 4

Overview

Absolute error, relative error and accumulated error.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Key term

What does truncation do, how does its error behave over many operations, how does rounding differ, and what is that error?

Key term

What is truncation?

Key term

Which introduces more error on average, truncation or rounding, and why?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is truncation?

    Model answer

    Discarding the digits that will not fit, without adjusting the digits that remain.

  2. 2

    What is rounding?

    Model answer

    Adjusting the last retained digit according to the value of the digits discarded.

  3. 3

    Which of the two introduces more error on average, and why?

    Model answer

    Truncation, because it always moves the value towards zero, so the errors accumulate in one direction.

  4. 4

    Why does rounding produce a smaller average error?

    Model answer

    The adjustment is upward about as often as downward, so errors tend to cancel over many operations.

  5. 5

    What is absolute error?

    Model answer

    The difference between the stored value and the true value.

  6. 6

    What is relative error?

    Model answer

    The absolute error expressed as a proportion of the true value.

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