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**Hint:**In astronomical physics, Light year is a unit used to measure distance. A light year is the distance which a light travels with the speed of light in vacuum which is $c = 3 \times {10^8}m{\sec ^{ - 1}}$ in one Year. This distance is called one light year.

**Complete step-by-step solution:**

Let us first understand the light year in brief and then compare its magnitude with one metre.

So, According to astronomical measurements the value of one light year can be calculated as:

Speed of light in vacuum is $c = 3 \times {10^8}m{\sec ^{ - 1}}$

The No. of seconds in year can simple be calculated as:

No. of seconds in a Julian year is $ = 3.15 \times {10^7}\sec $

So, the magnitude of one light year may be written as

$1$ Light year $ = 3 \times 3.15 \times {10^{15}}m$

$1$ Light year $ = 9.46 \times {10^{15}}m$

So we get to know that,

The value of one light year in metres is $ = 9.46 \times {10^{15}}m$ which means

In one light year there are $9.46 \times {10^{15}}m$ and in order to find number of light years in one metre we will simply divide this number by one and we can write it’s as:

Number of light years in one metre is equals to $\dfrac{1}{{9.46 \times {{10}^{15}}}}$

So, Number of light years in one metre is $1.05 \times {10^{ - 16}}$ Light years.

Hence, in one metre there are $1.05 \times {10^{ - 16}}$ Light years.

**Note:**In astronomical physics, all this distances are measured with the help of speed of light as this speed of light is constant for any observer and light also travel without any restriction in free space and also since, distances are to be measured between galaxies and stars which is quite large where we can’t use simple units we need larger units to define these distances hence, light year is used.

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