Question

3.$\overline {27}$ ia
(a) an integer
(b) a rational number
(c) a natural number
(d) an irrational number

Answer 1

Answer:

Among the given options option (b) a rational number  is a correct answer.

 

Step-by-step explanation:

 Given : 3.27 (bar on 27)

 Let x = 3.272727....   ------------- (1)

 On multiplying by 100 on both sides , we get  

 100 x = 3.272727…... (bar on 27)  

100x = 327.2727…….  -----------(2)

 

On Subtracting eq 1 from eq 2,  

 99 x = 324

 x = 324/99

 x = 108/33 = 36/33 = 12/11

 x = 12/11

 x = 1.090909......

x = 1.09….(bar on 09)

 Here , .09 repeated  again and again,so it is said to be non-terminating repeating decimal or recurring decimal expansion.

 Decimal expansion of every rational number is either terminating or not terminating repeating.

 

Hence, 3.27 (bar on 27) is a rational number.

 HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hey mate

Answer in attachment

3.72( bar on 27) is a rational number

Hope it help uh