Determine the Type of Number (3pi)/4

Problem

(3*π)/4

Solution

1. Identify the components of the expression. The expression consists of the integer 3 the mathematical constant π and the integer 4

2. Recall the definition of π The number π is an irrational number, meaning it cannot be expressed as a ratio of two integers and its decimal expansion is non-repeating and non-terminating.

3. Apply the properties of irrational numbers. Multiplying an irrational number by a non-zero rational number (3/4 results in an irrational number.

4. Classify the number within the real number system. Since it is irrational, it is also a real number and a complex number. Specifically, because it involves π it is a transcendental number (a number that is not the root of any non-zero polynomial equation with rational coefficients).

Final Answer

(3*π)/4=Irrational, Real, Transcendental

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