To determine if \(-2 \frac{9}{26}\) is an irrational number, we first need to convert it into a more standard form.
The mixed number \(-2 \frac{9}{26}\) can be converted to an improper fraction:
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Multiply the whole number \(-2\) by the denominator \(26\): \[ -2 \times 26 = -52 \]
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Add the numerator \(9\): \[ -52 + 9 = -43 \]
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Therefore, \(-2 \frac{9}{26} = \frac{-43}{26}\).
Now we analyze whether \(\frac{-43}{26}\) is an irrational number. A number is classified as irrational if it cannot be expressed as a fraction of two integers (i.e., it cannot be written in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b\) is not zero). Since \(-43\) and \(26\) are both integers and \(26 \neq 0\), we conclude that \(\frac{-43}{26}\) is a rational number.
Thus, \(-2 \frac{9}{26}\) is not an irrational number; it is a rational number.