$\frac{.009}{x} = .01$

## Concept & Formula This is a basic decimal division problem. The equation involves isolating the unknown variable $x$. $$ \text{Dividend} \div \text{Divisor} = \text{Quotient} $$ ## Step-by-Step Solution * **Given:** $\frac{0.009}{x} = 0.01$ * **Calculation:** Rearrange the equation to solve for $x$: $x = \frac{0.009}{0.01}$ Multiply the numerator and denominator by 1000 to remove decimals: $x = \frac{9}{10}$ Convert back to a decimal: $x = 0.9$ ## Exam Strategy & Shortcut When dividing decimals, focus on the shift of decimal places. You are dividing $0.009$ (3 decimal places) by $0.01$ (2 decimal places). The result will have $3 - 2 = 1$ decimal place. $9 \div 1 = 9$, with 1 decimal place makes it $0.9$. This allows you to solve the equation mentally in seconds. ## Common Pitfall The most common mistake is miscounting the decimal shifts, leading to $0.09$ or $9$. Always write out the powers of 10 if you are unsure, or cross-check by multiplying your answer by the quotient ($0.9 \times 0.01 = 0.009$). ## Final Answer **Therefore, the correct answer is .9.**