Question

express the following in the form p/q where p and q are integer and q is not equal to 0 (0.4777777.....)​

Answer 1

Answer:

Required numeric value of 0.47777... is 43 / 90.

Step-by-step-explanation:

Let the required value of 0.47777.... ( or 0.4$\bar{7}$ be x,

x = 0.4$\bar{7}$

After decimal, we are getting two numbers, one has bar on it while other is without bar. To remove that number ( which is without bar ), multiply both sides by 10.

Multiplying both sides by 10 .

= > 10 × x = 10 × 0.4$\bar{7}$

= > 10x = 4.$\bar{7}$ ---: ( i )

Now, as there is only one number under bar, multiply by 10 on both sides,

= > 10 × 10x = 10 × 4.$\bar{7}$

= > 100x = 47.$\bar{7}$

Subtracting ( i ) from this equation :

= > 100 x - 10x = 47.$\bar{7}$ - 4.$\bar{7}$

= > 90x = 43 [ bar cancel ]

= > x = 43 / 90

Hence the required numeric value of 0.47777... is 43 / 90