An irrational number is a number that cannot be expressed as a simple fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). This means that irrational numbers cannot be represented as the ratio of two integers.
To analyze your options:
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A fraction with 0 in the numerator: This equals 0, which is a rational number.
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A fraction with \( n \) as the numerator: If \( n \) is an integer and the denominator is also an integer (and non-zero), this fraction will be rational.
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A fraction with a negative integer as the numerator: Similar to the previous cases, if the denominator is a non-zero integer, this fraction is also rational.
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An improper fraction: An improper fraction can be expressed as the ratio of two integers (the numerator is greater than the denominator), and therefore it is rational.
None of the options provided can be considered an example of an irrational number, as all represent forms of rational numbers. An example of an irrational number would be something like \( \sqrt{2} \) or \( \pi \), which cannot be expressed as a fraction of two integers.
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