Determining rationality of real numbers represented by prime digit sequence

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Jiketz
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The problem describes a sequence of real numbers formed by arranging prime digits in a certain pattern. If the original real number is rational, then all subsequent numbers formed from its decimal expansion are also rational. However, there exists an irrational number with the same pattern whose subsequent numbers are still rational.
I would like to know if my answer is correct and if no ,could you correct.But it should be right I hope:
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Thread locked. The OP has been advised to repost the question in one of the homework forum sections.
 

FAQ: Determining rationality of real numbers represented by prime digit sequence

What is a prime digit sequence?

A prime digit sequence is a sequence of digits that consists only of prime numbers. The prime digits are 2, 3, 5, and 7. For instance, a sequence like 2357 or 7523 is made up entirely of these prime digits.

How can we determine if a real number represented by a prime digit sequence is rational?

A real number is considered rational if it can be expressed as a fraction of two integers. To determine if a number represented by a prime digit sequence is rational, we can examine its decimal representation. If the decimal representation terminates or eventually repeats, then the number is rational. Otherwise, it is irrational.

Are all real numbers formed from prime digit sequences rational?

No, not all real numbers formed from prime digit sequences are rational. While some combinations of prime digits may create rational numbers, many arrangements can lead to non-repeating and non-terminating decimal expansions, which are classified as irrational numbers.

What role do prime digits play in the properties of the number?

Prime digits themselves do not inherently determine the rationality of a number; rather, it is the structure of the number as a whole that matters. While prime digits can form various numbers, including both rational and irrational ones, their presence alone does not guarantee any particular property regarding rationality.

How does the concept of prime digit sequences relate to number theory?

Prime digit sequences relate to number theory in that they explore the properties and classifications of numbers based on their digits. This investigation can shed light on patterns and characteristics of numbers, potentially leading to insights about prime numbers, rationality, and the distribution of digits in numerical representations.

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