Question

answer for 8th question in that 4 one

Answer 1

(i) 0.555...
= 555...../ 1000.....
(ii) 3.8888...
= 388.../100.....
(iii) 0.363636...
= 3636...../10000....
(iv) 3.127777.....
= 31277../ 100000....

Answer 2

period = 7 
period city = 1
X =  3.12777 ( equation 1 ) 

multiply by 10 on the both right hand side and even left hand side of the equation 1 

⇒ 10 × X = 3.12777 × 10 
⇒ 10X = 31.2777  ( equation 2 )

now subtract equation 2 from equation 2 

⇒ 10X = 31.2777 ( - ) X = 3.1277 
⇒ 9X = 28.1500 
⇒ X = $\frac{28.15}{9}$

( here to remove the decimal point in the number 28.15 we need to multiply both the numerator and denominator with 100 ) 
 
⇒ X = $\frac{2815}{900}$ ( this is after multiplying with 100 ) 
⇒ X = $\frac{563}{180}$