The following real numbers have decimal | Class 10 Mathematics Chapter Real Numbers, Real Numbers NCERT Solutions

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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Welcome to the NCERT Solutions for Class 10 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 4 , Question 3: The following real numbers have decimal expansions as given below. In each case, decide whether they....