Question

The following real numbers have decimal expansion 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 1

i) 43.123456789 is terminating or rational

43.123456789=1000000000

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43123456789

=10943123456789=943123456789 = 43123456789

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10 root 9 (2×5) root 9 2root9×5root9

=29×5943123456789

This is in the form of qp, and the prime factors of q are in terms of 2 and 5.

ii) 0.120120012000120000.... is non-terminating and non-repeating, it is irrational. Hence cannot be expressed in the form of qp