Lesson 4.5.4.5

4.5.4.5 Rounding errors Quiz: AQA Computer Science, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 4.5.4.5, Rounding errors: 20 multiple choice questions for the AQA Computer Science (7517), Unit 5: Fundamentals of data representation, written with Revision Ninja.

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The 20 questions

  1. Why can decimal 0.1 not be stored exactly in a binary system?

    • It is negative
    • It is irrational
    • It recurs infinitely
    • It causes overflow

  2. What term describes the difference between an exact value and its stored approximation?

    • Syntax error
    • Truncation error
    • Overflow error
    • Rounding error

  3. Which binary representations can suffer from rounding errors when storing decimal fractions?

    • Fixed point only
    • Floating point only
    • Fixed and floating
    • Integers only

  4. When can a real number be represented exactly in a binary system?

    • As whole integer
    • As decimal fraction
    • As prime number
    • As binary fraction

  5. What is calculated by subtracting the stored approximation from the exact value?

    • Absolute error
    • Truncation error
    • Percentage error
    • Relative error

  6. How is relative error calculated using absolute error and the true value?

    • Absolute divided by true
    • Absolute minus true
    • True plus absolute
    • True divided by absolute

  7. A value of 0.8 is stored as 0.79. What is the absolute error?

    • 0.02
    • 0.79
    • 0.01
    • 0.1

  8. A value of 0.8 is stored as 0.79. What is the relative error?

    • 0.8
    • 0.0125
    • 1.25
    • 0.125

  9. An approximation of 1000 is given as 1003. What is the relative error?

    • 0.003
    • 0.3
    • 3
    • 0.03

  10. An absolute error of 0.1 occurs for values 0.5 and 1000. Which has the larger relative error?

    • Both are equal
    • Value 1000
    • Neither value
    • Value 0.5

  11. Using 2 fractional bits in fixed point, which value can be stored exactly?

    • 2.1
    • 2.75
    • 2.3
    • 2.6

  12. A value of 0.2 is stored as 0.1875 (0.0011 in binary). What is the absolute error?

    • 0.0125
    • 0.3875
    • 0.0075
    • 0.0250

  13. A value of 2.6 is stored in fixed point with 2 fractional bits, using the nearest representable value. What is stored, and what is the absolute error?

    • 2.6, with absolute error 0
    • 2.5, with absolute error 0.5
    • 2.75, with absolute error 0.15
    • 2.5, with absolute error 0.1

  14. A measurement of 50,000 has an absolute error of 5. What is the relative error?

    • 0.001
    • 0.0001
    • 0.1
    • 0.01

  15. If a true value of 10 is stored as 9.9, what is the absolute error?

    • 0.9
    • 1.0
    • 0.01
    • 0.1

  16. Why is relative error often more useful than absolute error?

    • Always gives integers
    • Ignores actual error
    • Eliminates rounding errors
    • Considers number magnitude

  17. What happens to small representation errors when performing many successive arithmetic operations?

    • They stay constant
    • They accumulate
    • They cancel out
    • They disappear

  18. A fixed point format with 3 fractional bits stores 1.3 as the nearest representable value. What are the stored value and the absolute error?

    • 1.5, with absolute error 0.2
    • 1.25, with absolute error 0.25
    • 1.375, with absolute error 0.075
    • 1.25, with absolute error 0.05

  19. A value of 0.0001 is stored as 0.0002. What is the relative error?

    • 0.5, or 50 percent
    • 1.0, or 100 percent
    • 0.0001, or 0.01 percent
    • 2.0, or 200 percent

  20. What happens to rounding errors when multiple calculations are chained together?

    • They stay constant
    • They accumulate
    • They cancel out
    • They vanish

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