To determine which of the given options is a rational number, let's analyze each one step-by-step:
1. The value of pi [tex]\((\pi)\)[/tex]:
- The value of π (pi) is approximately 3.14159...
- Pi is a well-known irrational number. It cannot be expressed as a fraction of two integers, and its decimal representation goes on forever without repeating.
- Conclusion: Pi is not a rational number.
2. Square root of 2 [tex]\((\sqrt{2})\)[/tex]:
- The square root of 2 is approximately 1.41421...
- √2 is also an irrational number. It cannot be expressed as a fraction of two integers, and its decimal representation is non-terminating and non-repeating.
- Conclusion: √2 is not a rational number.
3. Any decimal number:
- "Any decimal number" is a vague term. Decimal numbers can be either rational or irrational.
- A rational decimal number either terminates (like 0.75) or repeats (like 0.333...).
- However, irrational decimal numbers are non-terminating and non-repeating (like pi or √2).
- Without clarification, we cannot conclusively determine if "any decimal number" refers exclusively to rational numbers.
- Conclusion: The statement is too ambiguous to determine rationality.
4. [tex]\(\frac{9,731,245}{42,754,021}\)[/tex]:
- A fraction where both the numerator and the denominator are integers is a rational number by definition.
- Here, [tex]\(\frac{9,731,245}{42,754,021}\)[/tex] is a fraction composed of two integers.
- Conclusion: This fraction is indeed rational.
Final Answer:
The rational number among the given options is [tex]\(\frac{9,731,245}{42,754,021}\)[/tex], which corresponds to option 4.
