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$\begin{array}{l}{\text { Starting with the definition } 1 \text { in. }=2.54 \mathrm{cm}, \text { find the number }} \\ {\text { of }(\mathrm{a}) \text { kilometers in } 1.00 \text { mile and }(\mathrm{b}) \text { feet in } 1.00 \mathrm{km} .}\end{array}$

$1 inch=2.54 \mathrm{cm}$

$12 \text { inch }=1 \mathrm{Ft}$

$5280 \mathrm{ft}=1 \mathrm{mi}$

$1 m=100 \mathrm{cm}$

$1 k{m}=1000 m$

$m i \longrightarrow k m??$

$1 \mathrm{mi}=5280 \mathrm{Ft} * 12 \mathrm{in}=63360 \mathrm{in}$

$63360 \mathrm{in} * 2.54 \mathrm{cm}=160934 .4 \mathrm{cm}$

$160934.4 \mathrm{cm} \div 100=1609.344 \mathrm{m}$

$1609. 344 \mathrm{m} \div 1000=1.61 \mathrm{km}$

$km \rightarrow f t$

$1 \mathrm{km} * 10^{3} \mathrm{m}=1000 \mathrm{m}$

$1000 * 100=100000 \mathrm{cm}$

$\frac{100000}{2.54 \mathrm{cm}} * 12 \mathrm{in}=3.28*10^{3} \mathrm{ft}$

$\begin{array}{l}{\text { According to the label on a bottle of salad dressing, the }} \\ {\text { volume of the contents is } 0.43 \text { liter }(1) \text { . Using only the conversions } 1 \mathrm{L}=1000 \mathrm{cm}^{3}} \\ {\text { And } 1 \mathrm{in.}=2.54 \mathrm{cm}, \text { express this volume in cubic inches. }}\end{array}$

$1 L=1000 \mathrm{cm}^{3}$

$1 in= 2.54 \mathrm{cm}$

$L \rightarrow {in}^{3} ??$

$0.473 * 1000 \mathrm{cm}^{3}=473 \mathrm{cm}^{3}$

$\frac{473}{(2.54)^{3}}=28.9 \mathrm{in}^{3}$

$\begin{array}{l}{\text { How many nanoseconds does it take light to travel } 1.00 \mathrm{ft}} \\ {\text { in vacuum? (This result is a useful quantity to remember.) }}\end{array}$

$V=3 * 10^{8} \mathrm{m} / \mathrm{s}$

$1 f=0.3048 m$

$\rightarrow v=\frac{d}{t??} \rightarrow t=\frac{d}{V}=\frac{0.3048 \mathrm{m}}{3 * 10^{8} \mathrm{m} / \mathrm{s}}$

$∴ t=1.02 * 10^{-9} s \rightarrow 1.02 * 10^{-9} * 10^{9}=1.02 \mathrm{ns}$

$\begin{array}{l}{\text { The density of gold is } 19.3 \mathrm{g} / \mathrm{cm} 3 \text { What is this value in }} \\ {\text { kilograms per cubic meter? }}\end{array}$

$1 kg=1000 g$

$1m=100 c m$

$\frac{g}{c m^{3}} \rightarrow \frac{k g}{m^{3}}$

$19.3 \frac{g}{c m^{3}} * \frac{ 1 k g}{1000 g} *\left(\frac{100 \mathrm{cm}}{1 m }\right)^{3}$

$=19.3 * 10^{4} \frac{k g}{m^{3}}$