Exam-style question
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Explain the difference between using natural numbers for counting and using real numbers for measurement. Include one example of each.
Model answer
What a good answer should say
- Natural numbers are used to represent the number of separate items being counted, for example 18 books.
- Real numbers are used to represent measurements, which may include fractional values, for example 4.25 metres.
- Therefore, counting records how many items there are, whereas measurement records a quantity such as length that may not be a whole number.
Explanation
Why this works
A strong answer distinguishes the purpose of the values rather than relying only on whether a particular value happens to be a whole number. Counts are represented using natural numbers, while measurements are represented using real numbers so that fractional measurements can be represented.
Common mistake
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