To determine whether the number \( 9 + \pi \) is rational or irrational, we need to consider the properties of rational and irrational numbers.
A rational number is defined as any number that can be expressed as the quotient of two integers (i.e., \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)). An irrational number is a number that cannot be expressed as such a quotient.
The number \( \pi \) is known to be irrational. Since \( 9 \) is a rational number (it can be expressed as \( \frac{9}{1} \)), we look at the sum of a rational number and an irrational number:
- The sum of a rational number and an irrational number is always irrational.
Therefore, since \( 9 \) is rational and \( \pi \) is irrational, the sum \( 9 + \pi \) is irrational.
In conclusion, \( 9 + \pi \) is irrational.
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