Question

complete the following conversions using dimensional analysis. round to the significant figures.

1. convert 325 milligrams to grams.
2. convert 16.2 hours into seconds.
3. what is 37.50 pounds in milligrams?
4. an object is 7.25 feet long. what is this length in centimeters?

Explanation:

Step1: Convert milligrams to grams

We know that \(1\) gram \( = 1000\) milligrams. So, to convert \(325\) milligrams to grams, we use the conversion factor \(\frac{1\space g}{1000\space mg}\).

$$325\space mg\times\frac{1\space g}{1000\space mg}=\frac{325}{1000}\space g = 0.325\space g$$

Step2: Convert hours to seconds

We know that \(1\) hour \(= 60\) minutes and \(1\) minute \( = 60\) seconds. So the conversion factors are \(\frac{60\space min}{1\space h}\) and \(\frac{60\space s}{1\space min}\).

$$16.2\space h\times\frac{60\space min}{1\space h}\times\frac{60\space s}{1\space min}=16.2\times60\times60\space s = 58320\space s$$

Step3: Convert pounds to milligrams

First, \(1\) pound \(= 453.592\) grams (approximate conversion). Then \(1\) gram \(= 1000\) milligrams.
The conversion factors are \(\frac{453.592\space g}{1\space lb}\) and \(\frac{1000\space mg}{1\space g}\)

$$37.50\space lb\times\frac{453.592\space g}{1\space lb}\times\frac{1000\space mg}{1\space g}=37.50\times453.592\times 1000\space mg$$

$$=37.50\times453592\space mg=17009700\space mg$$

Step4: Convert feet to centimeters

We know that \(1\) foot \( = 12\) inches and \(1\) inch \(= 2.54\) centimeters. The conversion factors are \(\frac{12\space in}{1\space ft}\) and \(\frac{2.54\space cm}{1\space in}\)

$$7.25\space ft\times\frac{12\space in}{1\space ft}\times\frac{2.54\space cm}{1\space in}=7.25\times12\times2.54\space cm$$

$$=87\times2.54\space cm = 220.98\space cm$$

Answer:

1. \(0.325\space g\)
2. \(58320\space s\)
3. \(17009700\space mg\)
4. \(220.98\space cm\)