How many light years are there in one metre?

The correct option is 1.057x 10⁻¹⁶ ly.

To find the number of light years (ly) in one metre, we need to understand the relationship between a light year and a metre.

A light year is the distance that light travels in a vacuum in one Julian year. The speed of light (c) is approximately:
$c=3\times {10}^8\text{m/s}$

One year in seconds is:
$1\text{year}=365.25\times 24\times 60\times 60\text{seconds}��3.1536\times {10}^7\text{s}$

Therefore, one light year in metres is:
$1\text{ly}=(3\times {10}^8\text{m/s})\times (3.1536\times {10}^7\text{s})\approx 9.46\times {10}^{15}\text{m}$

Now, to find how many light years are in one metre, we take the reciprocal of this value:
$1\text{m}=\frac{1}{9.46\times {10}^{15}}\text{ly}$

Calculating the division gives:
$1\text{m}\approx 0.1057\times {10}^{-15}\text{ly}$

Expressing this in scientific notation to match the correct option:
$1\text{m}\approx 1.057\times {10}^{-16}\text{ly}$