Divide small decimals accurately Evaluate: 0.000033 ÷ 0.11 = ?

Introduction / Context:
Dividing very small decimals is easiest when you convert to fraction or scientific notation. This prevents place-value mistakes and makes mental checks straightforward.

Given Data / Assumptions:

• Compute 0.000033 / 0.11.
• Exact decimal values are intended; no rounding required.

Concept / Approach:
Use scientific notation: 0.000033 = 3.3 * 10^-5 and 0.11 = 1.1 * 10^-1. Then divide coefficients and subtract exponents. Alternatively, scale both numerator and denominator by 100 to remove decimals judiciously.

Step-by-Step Solution:
Write 0.000033 = 3.3 × 10^-5 and 0.11 = 1.1 × 10^-1.Divide: (3.3 / 1.1) × 10^(-5 − (−1)) = 3 × 10^-4.Convert to decimal: 3 × 10^-4 = 0.0003.

Verification / Alternative check:
As fractions, 0.000033 / 0.11 = (33/1,000,000) / (11/100) = (33/1,000,000) * (100/11) = 3/10000 = 0.0003. Matches the previous method.

Why Other Options Are Wrong:
.003, .03, .3: Each is 10, 100, or 1000 times too large, reflecting misplaced decimal points.

Common Pitfalls:
Moving the decimal in only the numerator or denominator; forgetting that division by 0.11 should increase the magnitude modestly but not drastically. Scientific notation helps keep track of powers of 10.

Final Answer:
0.0003