Question

Express the distance $150 \times {10^6}\,km$ in light years.

Answer 1

Hint: In order to solve this question, we will first know the definition of a light year. One light year is the distance travelled by light in one year. One light year is equal to $9.46 \times {10^{12}}\,km$. Now, we will be using the unitary method to express the given distance in light years. Suppose, we buy $5$ pencils for rupees $25$ and we want to know the price of $15$ pencils. So, in such a type of problem, we use a unitary method. So, we have, cost of five pencils $ = Rs\,25$
Cost of one pencil $ = Rs\,\dfrac{{25}}{5} = Rs\,5$
Now, cost of $15$pencils $ = 15 \times Rs\,5 = Rs\,75$

Complete step by step answer:
Now, we know that one light year is a unit of astronomical distance that light travels in one year. One light year is equal to $ = 9.46 \times {10^{12}}km$. So, we have,
$9.46 \times {10^{12}}\,km = 1$ light year
Now, finding the value of one kilometre in terms of a light year, we get,
$ \Rightarrow 1\,km = \dfrac{1}{{9.46 \times {{10}^{12}}}}$ light years
Now, we have to find the value of $150 \times {10^6}\,km$ in terms of light year. So, we multiply both sides of the equation by $150 \times {10^6}$.

Hence, we get,
$ \Rightarrow 150 \times {10^6}\,km = \dfrac{1}{{9.46 \times {{10}^{12}}}} \times 150 \times {10^6}$ light year
Simplifying the expression, we get,
$ \Rightarrow 150 \times {10^6}\,km = \dfrac{{15}}{{9.46 \times {{10}^5}}}$ light year
Doing the calculations, we get,
$\therefore 150 \times {10^6}\,km = 1.586 \times {10^{ - 5}}$ light year

So, $150 \times {10^6}\,km$is equivalent to $1.586 \times {10^{ - 5}}$ light years.

Note: Objects in our universe are extremely far away. Light year is used to measure astronomical distances. It is denoted by ly, and the value is $9.46 \times {10^{12}}km$. Mostly light years are used to measure distance from the star. Light moves at a velocity of about $3 \times {10^8}m/s$ which is the fastest moving stuff in our universe so, in one light year, it can travel about 10 trillion km.