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Class 10
Mathematics
Real Numbers
the following real numbers have decimal expansions...

Question:
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p/q what can you say about the prime factors of q?

Answer:

Note: A rational number has a decimal expansion which is either terminating or non -Terminating repeating otherwise the given number is irrational.

43.123456789

Since, the given decimal expansion is terminating. Therefore it is a rational number and we know that the prime factorization of denominator of rational 2 and 5 or both.

0.120120012000120000……

Since, the given decimal expansion is non- terminating non- repeating. Therefore it is irrational number.

Since, the given decimal expansion is non- terminating repeating. Therefore it is a rational number and we know that the prime factorization of denominator of rational 2 and 5 or both.

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Question:
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p/q what can you say about the prime factors of q?

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Question: The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p/q what can you say about the prime factors of q?

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Question:
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form , p/q what can you say about the prime factors of q?