Solve 0.0272727x - 3.49091 = 0 for x.

Step-by-step solution

1. 1

   Move the constant to the right. A single-step isolation:

   $0.0272727x=3.49091$

2. 2

   Divide by the coefficient.

   $x=\frac{3.49091}{0.0272727}=128.00016\ldots$

   That is suspiciously close to a whole number, which is worth investigating rather than reporting as-is.

3. 3

   Recognise the coefficients as rounded repeating decimals. $0.0272727\ldots$ is the decimal form of $\dfrac{3}{110}$, and $3.4909090\ldots$ is $\dfrac{384}{110}$. The problem statement simply truncated both at five or six places.

4. 4

   Redo the division with the exact fractions. The common denominator cancels outright:

   $x=\frac{384/110}{3/110}=\frac{384}{3}=128$

   So the residual $0.00016$ in step 2 is entirely an artefact of the rounded input, not a feature of the problem.

5. 5

   State both answers. Taking the printed decimals literally gives $x\approx 128.0002$; the intended exact answer is $x=128$. Whenever a decimal-coefficient equation lands within a rounding error of an integer, checking for hidden fractions like this is the right reflex.