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QuestionMathematics

Is (π+ 3.14) a rational number, an irrational number, or zero?
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Understand the components

- π is a well-known mathematical constant - 3.14 is a rational number (a decimal representation)

Step 3:
: Examine the properties of π

- π is a transcendental and irrational number - This means π cannot be expressed as a simple fraction of integers

Step 4:
: Analyze the sum (π+ 3.14)

- When we add an irrational number (π) to a rational number (3.14), the result remains irrational - This is because adding a rational number to an irrational number cannot make the irrational number rational

Step 5:
: Verify the result is not zero

- $$\pi + 3.14 \approx 6.28
- Clearly, this is not zero

Step 6:
: Classify the number

- Since (π+ 3.14) is the sum of an irrational number (π) and a rational number (3.14), the result is irrational - It is also not zero

Final Answer

(π+ 3.14) is an irrational number.