Question

Express 6.1977777..... in the form p/q, where p and q are integers and q is not equal to 0

Answer 1

GIVEN THAT 

X = 6.19777.....               
            _
X = 6.197            --------------(1)

SO, PERIODICITY = 1
10X = 61.9777.....              ------(2)

FROM (1) & (2)

10X = 61.97777....
-  X =   6.19777....
___________________
9X = 55.78

X = 55.78 / 9
X = 5578 /900
X = 2789 / 450

I.E P / Q = 2789 / 450

Answer 2


GIVEN ⇒× = 6.19777.....  
_
× = 6.197 --------------(1)
Multiply by 10 on both sides
10X = 61.9777..... ------(2)

Subtract 1 from 2 

⇒10X - X  = 61.97777....-  6.19777....
⇒9X = 55.78
⇒X = 55.78 / 9
⇒X = 5578 /900
⇒X = 2789 / 450
Thus,P/q= 2789 / 450