Q. 35.0( 3 Votes )

The following rea

Answer :


(i) 7.2345


Here, 7.2345 has terminating decimal expansion.


So, it represents a rational number.


i.e. 7.2345 = =


Thus, q = 104, those factors are 23 × 53


(ii)


is non-terminating but repeating.


So, it would be a rational number.


In a non-terminating repeating expansion of ,


q will have factors other than 2 or 5.


(iii) 23.245789


23.245789 is terminating decimal expansion


So, it would be a rational number.


i.e. 23.245789 = =


Thus, q = 106, those factors are 25 × 55


In a terminating expansion of , q is of the form 2n5m


So, prime factors of q will be either 2 or 5 or both.


(iv)


is non-terminating but repeating.


So, it would be a rational number.


In a non-terminating repeating expansion of ,


q will have factors other than 2 or 5.


(v) 0.120120012000120000…


0.120120012000120000… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


(vi) 23.142857


23.142857 is terminating expansion.


So, it would be a rational number.


i.e. 23.142857 = =


Thus, q = 106, whose factors are 25 × 55


In a terminating expansion of , q is of the form 2n5m


So, prime factors of q will be either 2 or 5 or both.


(vii) 2.313313313331…


2.313313313331… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


(viii) 0.02002000220002…


0.02002000220002… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


(ix) 3.300030000300003…


3.300030000300003… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


(x) 1.7320508…


1.7320508… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


(xi) 2.645713


2.645713 is terminating expansion


So, it would be a rational number.


i.e. 2.645713 = =


Thus, q = 106, those factors are 25 × 55


In a terminating expansion of , q is of the form 2n5m


So, prime factors of q will be either 2 or 5 or both.


(xii) 2.8284271…


2.8284271… is non-terminating and non-repeating.


So, it is not a rational number as we see in the chart.


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