Light travels at approximately 3.0*10^8 m/sec, How far does light travel in one week?

Jun 6, 2018

1.8 × 10^14\ "m"

Explanation:

Speed is given by

$\text{Speed" = "Distance"/"Time}$

From above

$\text{d = Speed × Time}$

color(white)("d") = 3 × 10^8\ "m/s" × "1 week"

$\textcolor{w h i t e}{\text{d") = 3 × 10^8\ "m/s" × 1 cancel"week" × "7 days"/(1 cancel"week}}$

$\textcolor{w h i t e}{\text{d") = 3 × 10^8\ "m/s" × 7 cancel"days" × "24 hrs"/(1 cancel"day}}$

$\textcolor{w h i t e}{\text{d") = 3 × 10^8\ "m/s" × 7 × 24 cancel"hrs" × "60 min"/(1 cancel"hr}}$

$\textcolor{w h i t e}{\text{d") = 3 × 10^8\ "m/s" × 7 × 24 × 60 cancel"min" × "60 s"/(1 cancel"min}}$

color(white)("d") = 3 × 10^8\ "m"/cancel"s" × 7 × 24 × 60 × 60 cancel"s"

color(white)("d") = 3 × 10^8\ "m" × 604800

color(white)("d") = 1814400 × 10^8\ "m"

color(white)("d") = 1.8144 × 10^14\ "m"

Light travelled 1.8 × 10^14\ "m" (in 2 significant figures) in a week.

Jun 6, 2018

~~1.8144 xx 10^14 " "m/("week")

Explanation:

Given: Light travels at $\approx 3.0 \times {10}^{8} \frac{m}{s}$

Use dimensional analysis to find the answer:

$3.0 \times {10}^{8} \frac{m}{s} \times \left(60 \text{ s")/"min" xx (60 " min")/h xx (24 " " h)/("day") xx (7 " days")/("week}\right)$

$= 3.0 {\left(60\right)}^{2} \left(24\right) \left(7\right) \times {10}^{8} = 1 , 814 , 400 \times {10}^{8}$

$= 1.8144 \times {10}^{6} \times {10}^{8}$

$= 1.8144 \times {10}^{6 + 8}$

= 1.8144 xx 10^14" "m/("week")