According to dimensional analysis, which of the following is the correct setup for the problem "How many milligrams are there in 67 kilograms?"

A. 67 kg = \([1 \, \text{g}/10^3 \, \text{kg}] \times [1 \, \text{mg}/10^{-3} \, \text{g}]\)

B. 67 kg = \([10^3 \, \text{kg}/1 \, \text{kg}] \times [10^{-3} \, \text{g}/1 \, \text{mg}]\)

C. 67 kg = \([10^3 \, \text{kg}/1 \, \text{kg}] \times [1 \, \text{mg}/10^{-3} \, \text{g}]\)

D. 67 kg = \([1 \, \text{g}/10^3 \, \text{kg}] \times [10^{-3} \, \text{g}/1 \, \text{mg}]\)

The correct set-up for the problem is option d: 67 kg = [1g/10³ kg]x[10⁻³ g/1 mg]. By using dimensional analysis and converting the units using the appropriate conversion factors, we can find that there are 67,000 milligrams in 67 kilograms.

Explanation:

The correct set-up for the problem "How many milligrams are there in 67 kilograms?" can be represented by option d: 67 kg = [1g/10³ kg]x[10⁻³ g/1 mg].

Dimensional analysis is a mathematical technique used to convert units from one system to another by using conversion factors. In this problem, we have to convert kilograms to milligrams. Since 1 kilogram is equal to 10³ grams and 1 gram is equal to 10⁻³ milligrams, we can set up the equation using these conversion factors.

By multiplying the conversion factors in the correct order, we can cancel out the units and calculate the final answer: 67 kg * (1 g / 10³ kg) * (10⁻³ mg / 1 g) = 67 * 10³ * 10⁻³ mg = 67,000 mg.

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