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CBSE Class 10 Answered

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
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