$4.036$ divided by $0.04$ gives

### Concept & Strategy To divide a decimal by another decimal, the most reliable strategy is to eliminate the decimal points by multiplying both the numerator and the denominator by the same power of 10. $$ \frac{a}{b} = \frac{a \times 10^n}{b \times 10^n} $$ ### Step-by-Step Solution * Write the division as a fraction: $$ \frac{4.036}{0.04} $$ * Multiply both the numerator and the denominator by $1000$ to remove the decimals completely (or multiply by $100$ to make the denominator a whole number): $$ \frac{4.036 \times 100}{0.04 \times 100} = \frac{403.6}{4} $$ * Perform standard division: $$ 403.6 \div 4 = 100.9 $$ ### Exam Strategy & Shortcut Instead of writing out the full fraction, simply shift the decimal point in both numbers to the right by two places (the number of decimal places in the divisor $0.04$). This immediately changes the problem from $4.036 \div 0.04$ to $403.6 \div 4$. Dividing $400$ by $4$ is $100$, and $3.6$ by $4$ is $0.9$, yielding $100.9$ instantly. ### Common Pitfall Students often misplace the decimal point during direct division, incorrectly answering $10.09$ or $1.009$. Always convert the divisor (the number you are dividing by) into a whole number first to avoid alignment errors. ### Final Answer **Therefore, the correct answer is 100.9.**