Q76E - Chemistry (OpenStax)

Question

Question:  Make the conversion indicated in each of the following:

(a) the men’s world record long jump, 29 ft 4¼ in., to meters

(b) the greatest depth of the ocean, about 6.5 mi, to kilometers

(c) the area of the state of Oregon, 96,981 mi², to square kilometers

(d) the volume of 1 gill (exactly 4 oz) to milliliters

(e) the estimated volume of the oceans, 330,000,000 mi³, to cubic kilometers.

(f) the mass of a 3525-lb car to kilograms

(g) the mass of a 2.3-oz egg to grams

Step-by-Step Solution

Answer

1. 8.95 m
2. 10.4607 km
3. 2.5118   10⁵ km²
4. 118.3 mL
5. 1.4   10⁹ km³
6. 1599 kg
7. 65 g

Step 1: Defining the conversion factor

It is the relationship between the units of the quantity that converts the units without changing the magnitude of the quantity.

The basic design of the conversion factor

\({\rm{Desired}}\,{\rm{unit}}\,\,{\rm{ = }}\,\,\frac{{{\rm{Desired}}\,{\rm{unit}}}}{{{\rm{Given}}\,{\rm{unit}}}}\,\,{\rm{ \times }}\,\,{\rm{Given}}\,{\rm{unit}}\)

These are used widely to convert the units. 

Step 2: Converting the unit from given quantities into required quantities

      a.    the men’s world record long jump, 29 ft 4¼ in., to meters

 

Adding, we get

\(\begin{array}{c}8.8392\,m\,\, + \,\,0.10795\,\,m\,\, = \,\,8.94715\,\,m\\ \approx 8.95m\end{array}\)

       b.   the greatest depth of the ocean, about 6.5 mi, to kilometers

\(\begin{array}{c}6.5\,\,miles\,\, = \,\,6.5\,\,\left( {miles\,\, \times \,\,\frac{{1.60934\,\,km}}{{miles}}} \right)\,\,\\ = \,\,10.4607\,\,km\end{array}\)

        c.   the area of the state of Oregon, 96,981 mi², square kilometers\(\begin{array}{c}96,981\,\,mile{s^2}\,\, = \,\,96,981\,\,mile{s^2}\, \times \,\,\frac{{2.5899\,\,k{m^2}}}{{mile{s^2}}}\,\,\\ = \,\,2,51,171.0919\,\,k{m^2}\,\,\\ = \,\,2.511717\,\, \times \,\,{10^5}\,k{m^2}\end{array}\)

        d.   the volume of 1 gill (exactly 4 oz) to milliliters

\(\begin{array}{l}1\,gill\,\, = \,\,4\,ounce\\\,\, = \,\,4\,\,\left( {ounce\,\, \times \,\frac{{29.5735\,\,mL}}{{ounce}}} \right)\,\\\, = \,\,118.294\,\,mL\\ \approx 118.3\,mL\end{array}\)

         e.   the estimated volume of the oceans, 330,000,000 mi3, to cubic kilometers

\(\begin{array}{c}333,000,000\,\,m{i^3}\,\, = \,\,333,000,000\,\,\left( {m{i^3}\, \times \,\frac{{4.18\, \times \,{{10}^9}\,{m^3}}}{{m{i^3}}}} \right)\,\\\, = \,\,333,000,000\,\, \times \,\,4.18\,\, \times \,{10^9}\,{m^3}\,\\\, = \,\,1.375\, \times \,{10^{18}}\,{m^3}\\ \approx \,\,1.4\, \times \,{10^{18}}\,{m^3}\end{array}\)

         f.   the mass of a 3525-lb car to kilograms

\(\begin{array}{c}3525\,lb\,\, = \,\,3525\,\,\left( {lb\, \times \,\frac{{0.4535\,\,kg}}{{lb}}} \right)\,\,\\ = \,\,1598.913\,\,kg\end{array}\)

        g.   the mass of a 2.3-oz egg to grams

\(\begin{array}{l}2.3\,\,ounce\,\, = \,\,2.3\,\left( {ounce\, \times \,\frac{{28.3495\,g}}{{ounce}}} \right)\,\,\\ = \,\,65.2039\,g\\ \approx 65g\end{array}\)