QQuestionMathematics
QuestionMathematics
"How do I convert 200 yards into meters using dimensional analysis? Explain thoroughly.
A) 200 yards×0.9144 meters/yard
B) 200 yards×1.0936 meters/yard
C) 200 yards×0.3048 meters/yard
D) 200 yards×0.0254 meters/yard"
12 months agoReport content
Answer
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Step 1:I'll solve this problem step by step using dimensional analysis:
Step 2:: Identify the Conversion Factor
The correct conversion factor from yards to meters is $$0.9144 \text{ meters/yard}$$.
This is a standard conversion factor used in length unit conversions.
Step 3:: Set Up the Dimensional Analysis Calculation
200 \text{ yards} \times \frac{0.9144 \text{ meters}}{1 \text{ yard}}
We'll multiply the given value by the conversion factor:
Step 4:: Cancel Out Units and Calculate
200 \times 0.9144 = 182.88 \text{ meters}
Step 5:: Verify the Calculation
- The units cancel out: $$\text{yards} \times \frac{\text{meters}}{\text{yard}} = \text{meters}
- The numerical calculation is: 200 \times 0.9144 = 182.88
Final Answer
Key Insights: - Dimensional analysis allows precise unit conversion - Always use the correct conversion factor - Carefully check that units cancel out - The correct answer is option A
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