Brackets and “of” in decimal expressions Evaluate: [12 / (0.09 of 0.3)] × 2 = ?

Introduction / Context:
This exercise combines bracket precedence with the word “of” meaning multiplication. Correctly evaluating inner products before division and multiplication is crucial for accurate results in compound decimal problems.

Given Data / Assumptions:

• Expression: [12 / (0.09 of 0.3)] × 2.
• “of” means multiplication.
• Standard order: parentheses (or brackets), then division/multiplication left to right.

Concept / Approach:
First compute the inner product 0.09 * 0.3. Then divide 12 by that result. Finally multiply by 2. Avoid mixing integer intuition with decimal precision; keep exact values until the end.

Step-by-Step Solution:
Compute inner: 0.09 * 0.3 = 0.027.Divide: 12 / 0.027 = 444.444... (exactly 400/0.9 = 444.444...).Multiply by 2: 444.444... * 2 = 888.888... .

Verification / Alternative check:
Write as fractions: 0.09 = 9/100 and 0.3 = 3/10, so denominator = 27/1000. Then 12 / (27/1000) = 12 * (1000/27) = 12000/27 = 444.444..., and doubling gives 888.888....

Why Other Options Are Wrong:
0.8, 0.08, 8: Each is orders of magnitude too small; they ignore the very small denominator 0.027 which inflates the quotient.

Common Pitfalls:
Treating “of” as addition or neglecting bracket precedence; rounding intermediate steps too early. Keep the exact fraction form until the final step to avoid compounding errors.

Final Answer:
None of these (the exact value is 888.888...).