Question

The speed of light is $3\times {10}^8$ meters/sec. If light takes $500$ seconds to travel from the Sun to the Earth, what is the distance in meters between the Sun and the Earth? Express your answer in scientific notation.$(\text{Use formula}:\text{Speed}=\frac{\text{Distance}}{\text{Time}})$

• A. $1.5\times {10}^{12}$ meters
• B. $1.5\times {10}^{10}$ meters
• C. $1.5\times {10}^{11}$ meters
• D. $1.5\times {10}^{13}$ meters

Answer 1

The correct option is C $1.5\times {10}^{11}$ meters

We know, Distance = Time $\times$ Speed

Hence, distance between the Sun and the Earth
$=$ Speed of light $\times$ Time taken to travel from the Sun to the Earth
$=3\times {10}^8\times 500$ meters
$=3\times {10}^8\times 5\times {10}^2$ meters
$=15\times {10}^{8+2}$ meters
$=15\times {10}^{10}$ meters
$=(1.5\times 10)\times {10}^{10}$ meters
$=1.5\times 10\times {10}^{10}$ meters
$=1.5\times {10}^{1+10}$ meters
$=1.5\times {10}^{11}$ meters