If $\frac{547.527}{0.0082} = x$, then the value of $\frac{547527}{82}$ is

### Concept & Logic Shifting decimal places in a fraction alters its total value by powers of $10$. By converting decimals to integers, we can track these power shifts to find the new value. ### Step-by-Step Solution * Write the initial equation and convert decimals to fractions of $10$: $$ \frac{547.527}{0.0082} = x $$ $$ \frac{547527 \times 10^{-3}}{82 \times 10^{-4}} = x $$ * Simplify the exponents: $$ \frac{547527}{82} \times 10^{(-3 - (-4))} = x $$ $$ \frac{547527}{82} \times 10^{1} = x $$ * Isolate the required expression: $$ \frac{547527}{82} = \frac{x}{10} $$ ### Exam Strategy & Shortcut Count the decimal place changes from the given equation to the target equation. The numerator shifted right by $3$ places, while the denominator shifted right by $4$ places. The net effect on the left-hand side is a multiplication by $10$. Moving this multiplier to the right side results in division by $10$. ### Common Pitfall Getting the sign of the power of $10$ reversed during isolation, mistakenly concluding the answer is $10x$. Always write out the negative exponents explicitly to avoid this. ### Final Answer **Therefore, the correct answer is $\frac{x}{10}$.**