1.236576576...
can be written in the form of:

Correct option is C

Solution:

$$\text{Let } x = 1.23657657657 \ldots \\\therefore x \text{ can be written as } x = 1.23657 \quad \text{----(A)} \\\text{This number has three repeating numbers, so we will multiply } 10^2 \text{ in equation (A)} \\100x = 123.657 \quad \text{----(1)} \\\text{Again, multiply } 10^5 \text{ in equation (A)} \\100000x = 123657.657 \quad \text{----(2)} \\\text{Subtract equation (1) from equation (2):} \\\Rightarrow 99900x = 123534 \\\therefore x = \frac{123534}{99900}$$​