Answer

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**Hint:**We have given 0.111 is approximately equal to $\dfrac{1}{9}$ and we are asked to find the approximate value for 0.777 which we are going to find by multiplying 7 by 0.111 and also multiplying 7 by $\dfrac{1}{9}$. Now, do the calculation of multiplication and find the correct option.

**Complete step-by-step solution:**

In the above problem, we have given that 0.111 is approximately equal to $\dfrac{1}{9}$ and the mathematical expression for this statement is equal to:

$0.111\approx \dfrac{1}{9}$

Now, to find the value of 0.777, we are going to multiply 7 on both the sides of the above equation and we get,

$7\left( 0.111 \right)\approx 7\left( \dfrac{1}{9} \right)$

Multiplying 7 by 0.111 on the L.H.S of the above equation and 7 by $\dfrac{1}{9}$ on the R.H.S of the above equation we get,

$\left( 0.777 \right)\approx \left( \dfrac{7}{9} \right)$

From the above equation, we got the approximate value of 0.777 which is equal to $\dfrac{7}{9}$.

**Now, the option which is equivalent to $\dfrac{7}{9}$ is equal to (b). Hence, the correct option is (b).**

**Note:**You might be thinking that how we know what number to multiply with 0.111 so that we will get the number 0.777. The answer is when we multiply 0.111 by 7 then we get 0.777 and multiplying 7 by 0.111 is an easy multiplication. So, an easy multiplication will quickly make you think that we should multiply 7 by 0.111. Also, don’t divide 7 by 9 because $\dfrac{7}{9}$ is a fraction given in the option and we can easily pick that right option.

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