Question

A light year is the distance that light can travel in one year.
$1$ light year $=9,460,000,000,000km.$
(a) Express one light year in scientific notation.
(b) The average distance between Earth and Sun is $1.496\times {10}^{8}km.$ Is the distance between earth and Sun greater than, less than or equal to one light year?

Answer 1

(a) Given, $1$ light year $=9,460,000,000,000km$
For standard form
$=946\times {10}^{10}km=\frac{946}{100}\times {10}^{10}\times 100km=9.46\times {10}^{12}km$

(b) The average distance between Earth and Sun $=1.496\times {10}^{8}km$
$\therefore$ Distance between Earth and Sun $=\frac{1.496}{10000}\times {10}^8\times {10}^{4}km=0.0001496\times {10}^{12}km$

Since, $9.46\times {10}^{12}>0.0001496\times {10}^{12}$
So, the distance between Earth and Sun is less than one light year.