Percentage conversion and scaling: Evaluate (0.756 × 3/4) and express the result as a rate percent.

Introduction / Context:This problem checks comfort with decimal–fraction multiplication and converting the final value into a percentage. The phrase “rate percent” simply means “express the numerical value as a percent.”

Given Data / Assumptions:

• Expression to compute: (0.756) * (3/4).
• Convert the final decimal to a percent by multiplying by 100.
• No rounding instruction is given; the multiplication yields an exact terminating decimal.

Concept / Approach:First multiply the decimal and the fraction. Then convert the resulting decimal into percent. Remember: x as a percent = x * 100%.

Step-by-Step Solution:

Verification / Alternative check:Another path: 3/4 of 0.756 means take 75% of 0.756. Ten percent of 0.756 is 0.0756, so 70% is 0.5292, and 5% is 0.0378. Add: 0.5292 + 0.0378 = 0.567. Then to percent: 56.7%.

Why Other Options Are Wrong:

• 18.9% and 37.8% correspond to taking 1/4 or 1/2 instead of 3/4.
• 75% confuses the fraction 3/4 with the final numeric result.
• 42.5% is an arbitrary distractor not supported by the computation.

Common Pitfalls:Mixing the order of operations or forgetting to convert the final decimal to percent. Keep the multiplication separate from the percent conversion step.

Final Answer:56.7%