To determine the type of number that the product \( \frac{4}{5} \cdot \pi \) will be, we need to analyze the two components involved in the multiplication.
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Fraction \( \frac{4}{5} \): This is a rational number. A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers (and the denominator is not zero).
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Number \( \pi \): The number \( \pi \) (approximately 3.14159) is an irrational number. An irrational number cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating.
When we multiply a rational number by an irrational number, the product is always an irrational number. This is because rational numbers can be represented as fractions, and multiplying an irrational number by a fraction results in a product that cannot be simplified to a fraction of integers.
Conclusion:
So, the product \( \frac{4}{5} \cdot \pi \) is an irrational number.