If $0.13 \div p^2 = 13$, then $p$ equals

Concept & Formula Rearrange the basic division equation to isolate the squared variable, then apply decimal division rules before extracting the square root. Step-by-Step Solution * **Given:** $\frac{0.13}{p^2} = 13$ * **Calculation:** Multiply both sides by $p^2$ and divide by $13$ to isolate $p^2$: $p^2 = \frac{0.13}{13}$ * Perform the division. You can rewrite the decimal as a fraction to make it visually easier: $p^2 = \frac{\frac{13}{100}}{13}$ $p^2 = \frac{13}{13 \times 100}$ $p^2 = \frac{1}{100}$ $p^2 = 0.01$ * Take the square root of both sides to find $p$: $p = \sqrt{0.01}$ $p = 0.1$ Exam Strategy & Shortcut Look at the significant digits. $13$ divided by something becomes $13$, meaning the divisor must just be shifting decimal places. Specifically, $0.13$ has to be divided by $0.01$ to shift the decimal two places to the right to become $13$. Thus, $p^2 = 0.01$. The square root of $0.01$ is $0.1$. Common Pitfall Failing to properly account for the decimal places when extracting the root, often mistakenly choosing option (a) $0.01$ because they forget that $p^2 = 0.01$, not $p$. Final Answer **Therefore, the correct answer is 0.1.**