Question

A;b are two single digit natural numbers such that 0.ababab... =8/11. find the value of a+b​

Answer 1

The value of a+b​ is 9

Step-by-step explanation:

• Given data

        a and b are single digit number

        $\mathbf{0.ababababab... = \frac{8}{11}}$         ...1)

• Multiply by 100 on both side, we get

        $\mathbf{ab.abababab... = \frac{800}{11}}$          ...2)

• Subtracting equation 1) from equation 2)

        $\mathbf{ab.abababab... -0.ababababab...=\frac{800}{11}- \frac{8}{11}}$

        $\mathbf{ab=\frac{800-8}{11}}$

        $\mathbf{ab=\frac{792}{11}=72}$

• We can say that

        a =7    and b =2

        So

        a + b = 7 + 2 = 9

Answer 2

(a + b) = 9

Step-by-step explanation:

We have, 0.ababab...... = $\frac{8}{11}$ ............. (1)

Now, we have to find the values of a and b.

Multiplying the above equation by 100 we get,

ab.ababab..... = $\frac{800}{11}$.

Now, we have to divide 800 by 11.

11 ) 800 ( 72

     77

------------

       30

       22

-------------

         8

Therefore, the process of division will continue as the remainder is 8 again.

From, this result we can conclude that a = 7 and b = 2

So, (a + b) = 7 + 2 = 9 (Answer)