Solving the Decimal Fraction Equation for x

We are given the equation: $ \frac{121}{0.121} = \frac{12.1}{x} $ Our goal is to find the value of $x$.

Step 1: Simplify the Left Side

First, let's simplify the fraction on the left side of the equation:

$ \frac{121}{0.121} = \frac{121}{\frac{121}{1000}} = 121 \times \frac{1000}{121} = 1000 $

So, the equation simplifies to:

$ 1000 = \frac{12.1}{x} $

Step 2: Isolate x

Now, we rearrange the equation to solve for $x$. Multiply both sides by $x$:

$ 1000 \times x = 12.1 $

Then, divide both sides by $1000$:

$ x = \frac{12.1}{1000} $

Step 3: Calculate the Final Value

Performing the division gives us the value of $x$:

$ x = 0.0121 $

Thus, the value of $x$ is $0.0121$.