Question

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

q

p

, what can you say about the prime factors of q ?(5)

i) 4.739br ii) 11.11111........ iii) 13.131331333

iv) 43.123456789 v) 0.03587bar​

Answer 1

$i) 4.73\bar{9} \: \blue { ( Rational \:number )}$

$It \: is \: a \:non - terminating \: recurring \\ decimal$

$ii) 11.111111\ldots \: \blue { ( Rational \:number )}$

$It \: is \: a \:non - terminating \: recurring \\ decimal$

$iii) 13.131331333 \: \blue { ( Rational \:number )}$

$It \: is \: a \: terminating \: decimal.$

$iv) 43.123456789 \: \blue { ( Rational \:number )}$

$It \: is \: a\: terminating \: decimal.$

$v ) 0.03587bar \: \blue { ( Rational \:number )}$

$It \: is \: non - terminating \: recurring \\ decimal$

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