Question

Carry out the following conversions: (a) 1.42 light-years to miles (a light-year is an astronomical measure of distance—the distance traveled by light in a year, or 365 days; the speed of light is 3.00 × 108 m/s). (b) 32.4 yd to centimeters. (c) 3.0 × 1010 cm/s to ft/s.

Answer 1

a) $1.42\space{l.y.}=1.42\ years\times\frac{3.00\times10^8\ m}{1\ s}\times\frac{1\ mi}{1609\ m}\times\frac{3600\ s}{1\ hr}\times\frac{24\ hrs}{1\ day}\times\frac{365\ days}{1\ year}=8.35\times10^{12}\ mi$

Answer: $8.35\times10^{12}\ mi$

b)

$32.4\ yd\times\frac{0.9144\ m}{1\ yd}\times\frac{100\ cm}{1\ m}=2.96\times10^3\ cm$

Answer: $2.96\times10^3\ cm$

c)

$3.0\times10^{10}\ \frac{cm}{s}\times\frac{1\ ft}{0.3048\ m}\times\frac{1\ m}{100\ cm}=9.8\times10^8\ \frac{ft}{s}$

Answer: $9.8\times10^8\ \frac{ft}{s}$