$.04 \times x = .000016$

### Concept & Formula When dealing with very small decimals, tracking the number of decimal places or converting the numbers into fractions limits the risk of alignment errors during division. $$ x = \frac{a}{b} $$ ### Step-by-Step Solution * **Given:** $$ 0.04 \times x = 0.000016 $$ * **Calculation:** Isolate the unknown variable $x$. $$ x = \frac{0.000016}{0.04} $$ * Multiply both the numerator and denominator by $100$ to clear the decimal point in the denominator (shifting the decimal two places to the right). $$ x = \frac{0.000016 \times 100}{0.04 \times 100} $$ $$ x = \frac{0.0016}{4} $$ * Divide $0.0016$ by $4$. $$ 0.0016 \div 4 = 0.0004 $$ ### Exam Strategy & Shortcut Use the "decimal place subtraction" rule for multiplication. The target product ($0.000016$) has 6 decimal places. The given multiplier ($0.04$) has 2 decimal places. Therefore, the unknown factor must have $6 - 2 = 4$ decimal places. Since $16 \div 4 = 4$, the answer is simply a $4$ placed with 4 decimal places, which writes exactly as $0.0004$. ### Common Pitfall Miscounting the zeros during standard long division. Under time pressure, it's easy to accidentally answer $0.04$ or $0.004$ by rushing the calculation. Relying strictly on counting decimal places entirely eliminates this risk. ### Final Answer **Therefore, the correct answer is 0.0004.**