Difficulty: Easy
Correct Answer: 0.060851
Explanation:
Introduction / Context:
This problem asks you to combine accurate decimal multiplication with a simple linear adjustment. The key is to compute the product exactly, then determine the small difference needed to reach the target value of 1.
Given Data / Assumptions:
Concept / Approach:
First multiply the decimals precisely. Then rearrange the equation to x = (0.527 × 2.013) − 1. Small digit errors derail the result, so compute carefully or break the multiplication into parts (0.5, 0.02, 0.007 components) for reliability.
Step-by-Step Solution:
Compute 2.013 × 0.527 = (2.013 × 0.5) + (2.013 × 0.02) + (2.013 × 0.007).= 1.0065 + 0.04026 + 0.014091 = 1.060851.Set 1.060851 − x = 1, hence x = 1.060851 − 1 = 0.060851.
Verification / Alternative check:
Direct multiplication confirms 1.060851. Subtracting 0.060851 indeed gives exactly 1.
Why Other Options Are Wrong:
Common Pitfalls:
Dropping digits in the product, or subtracting in the wrong direction (adding to reach 1 instead of subtracting from the product).
Final Answer:
0.060851
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