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Ex 1.4, 3 Decimal expansion of 43.123456789 ,0.12012001 - Decimal Expansion

  1. Chapter 1 Class 10 Real Numbers
  2. Serial order wise
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Ex 1.4 , 3 (Method 1) 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 , ๐‘/๐‘ž what can you say about the prime factors of q? 43.123456789 43.123456789 is terminating So, it would be a rational number 43.123456789 = 43123456789/1000000000 = 43123456789/(10)9 = 43123456789/(2 ร—5)9 = 43123456789/(29 ร—59) Hence 43.123456789 is now in the form of ๐‘/๐‘ž And the prime factors of q are in terms of 2 and 5 Ex 1.4 , 3 (Method 2) 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 , ๐‘/๐‘ž what can you say about the prime factors of q? 43.123456789 43.123456789 is terminating So, it would be a rational number In a terminating expansion of ๐‘/๐‘ž, q is of the form 2n 5m So, prime factors of q will be 2 or 5 or both only. Ex 1.4 , 3 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 , ๐‘/๐‘ž what can you say about the prime factors of q? (ii) 0.120120012000120000โ€ฆ 0.120120012000120000โ€ฆ is non terminating and non repeating So, it is not a rational number Ex 1.4 , 3 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 , ๐‘/๐‘ž what can you say about the prime factors of q? (iii) 43. ("123456789" )ย ฬ… Here 43. ("123456789" )ย ฬ… is non terminating but repeating. So, it would be a rational number In a non- terminating , repeating expansion of ๐‘/๐‘ž, q will have factors other than 2 or 5.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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