Evaluate the decimal expression 0.55 × 4.5 ÷ 0.81 by correctly applying multiplication and division operations.

Introduction / Context:
This numerical aptitude question checks the ability to handle multiplication and division with decimal numbers. Instead of immediately reaching for a calculator, a strong candidate converts decimals to fractions and simplifies the expression systematically. Doing so often leads to a neat rational result, which can be compared directly with fractional options and decimal options.

Given Data / Assumptions:

• Expression: 0.55 × 4.5 ÷ 0.81.

• All numbers are real, and the operations follow the usual left to right rule for multiplication and division.

• The final answer should match one of the provided options, which include fractions and decimals.

Concept / Approach:
A convenient method is to convert each decimal into a fraction with a power of 10 in the denominator. This converts the problem to a fraction multiplication and division task. Multiplication of fractions is straightforward: multiply numerators and denominators separately, then simplify. Division by a fraction is handled as multiplication by its reciprocal. After simplification, we can compare our fraction with the given fraction options or convert it to a decimal as a check.

Step-by-Step Solution:
Step 1: Express 0.55 as a fraction: 0.55 = 55/100 = 11/20 after simplification. Step 2: Express 4.5 as a fraction: 4.5 = 45/10 = 9/2 after simplification. Step 3: Express 0.81 as a fraction: 0.81 = 81/100 = 81/100. Step 4: Rewrite the expression: 0.55 × 4.5 ÷ 0.81 = (11/20) × (9/2) ÷ (81/100). Step 5: First multiply the fractions: (11/20) × (9/2) = 99/40. Step 6: Now divide by 81/100, which is the same as multiplying by 100/81, so we get (99/40) × (100/81). Step 7: Simplify: 99 and 81 have common factor 9, so 99/81 = 11/9. The product becomes (11/40) × 100/9. Step 8: Simplify further: 100/40 = 5/2, so we have 11 × (5/2) × (1/9) = 55 / 18.

Verification / Alternative check:
We can roughly check the magnitude by computing approximate decimals. 0.55 × 4.5 ≈ 2.475. Dividing by 0.81 gives about 2.475 ÷ 0.81 ≈ 3.0556. Converting 55/18 to decimal form: 55 ÷ 18 ≈ 3.0556, which perfectly matches. This confirms that the fraction 55/18 is indeed the exact simplified value of the original expression.

Why Other Options Are Wrong:
Option 3.555 is larger than 3.0556 and would require a larger numerator or smaller denominator in the fraction. Option 3.05 is close but slightly smaller than the true value and likely comes from premature rounding during intermediate steps. Option 55/81 is a completely different fraction whose decimal value is about 0.679, far from the correct magnitude. Option 3.25 equals 13/4 and does not match the exact computation. Only 55/18 matches both the exact fraction and the decimal approximation.

Common Pitfalls:
A common error is to multiply and divide decimals directly without carefully tracking place values, which leads to misplaced decimal points. Another mistake is treating the division by 0.81 as dividing by 81 instead of 81/100. Also, some students incorrectly cancel digits rather than factors when simplifying fractions. Converting all decimals to fractions and simplifying step by step is a reliable approach that avoids these issues.

Final Answer:
The correct value of the expression 0.55 × 4.5 ÷ 0.81 is 55/18.