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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 write prime factors of q so that p and q are co-primes. (a) 43.123 (b) 0.120120012000........ (c) 43.123123123123........
Asked by susrisangita792 | 02 Apr, 2023, 11:51: AM
answered-by-expert Expert Answer
(a) 43.123    (b) 0.120120012000........       (c) 43.123123123123........
left parenthesis straight a right parenthesis Let space straight m equals space 43.123 It space is space straight a space terminating space decimal space number space and space so space straight a space rational space number. rightwards double arrow straight m equals 43123 over 100 left parenthesis straight b right parenthesis 0.120120012000.... It space is space nether space terminating space nor space repeating. So comma space it space is space not space straight a space rational space number. left parenthesis straight c right parenthesis Let space straight n equals 43.123123123123...... space space space space space space space left parenthesis 1 right parenthesis It space is space non minus terminating space and space reapeating space decimal space and space so space straight a space rational space number. rightwards double arrow 1000 straight n equals 43123.123123123...... space space space space space space space space left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis space minus space left parenthesis 1 right parenthesis rightwards double arrow 999 straight n equals 43080 rightwards double arrow straight n equals 43080 over 999
Answered by Renu Varma | 10 Apr, 2023, 09:19: AM

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