If $\frac{1}{6.198} = 0.16134$, then the value of $\frac{1}{0.0006198}$ is

### Concept & Logic Moving the decimal point in the denominator of a fraction results in an inverse shift in the overall value of the fraction. ### Step-by-Step Solution * The given relation is: $$ \frac{1}{6.198} = 0.16134 $$ * We need to find the value of: $$ \frac{1}{0.0006198} $$ * Relate the new denominator to the given denominator: $$ 0.0006198 = 6.198 \times 10^{-4} $$ * Substitute this back into the target fraction: $$ \frac{1}{6.198 \times 10^{-4}} = \frac{1}{6.198} \times \frac{1}{10^{-4}} $$ $$ = 0.16134 \times 10^{4} $$ * Multiply by $10000$ (shift the decimal $4$ places to the right): $$ = 1613.4 $$ ### Exam Strategy & Shortcut The denominator decreased by $4$ decimal places (from $6.198$ to $0.0006198$). Making a denominator smaller makes the overall fraction larger. Shift the decimal point of the given answer ($0.16134$) exactly $4$ places to the right to compensate. ### Common Pitfall Multiplying the given value by $10^{-4}$ instead of $10^{4}$. Remember that a smaller denominator yields a larger result. ### Final Answer **Therefore, the correct answer is $1613.4$.**