Question

Calculate the number of astronomical units in one metre.

Answer 1

Hint: The given problem can be solved by finding the value for a single unit and then we need to multiply the single unit value to the number of units to get the necessary value.

Complete step by step answer:
We know the value of one light year. The value of one light year is given as,
$\Rightarrow 1AU=1.5\times {10}^{11}m$
Where $AU$ is known as Astronomical unit
Astronomical unit is the unit that is basically used to measure the large distances like between the sun and the planets, and the distance between the stars.
Here we have to use the method for unitary to solve the given problem. The unitary method is the method that is used for finding the value of a single unit. We need to multiply the single unit value to the number of units to get the desired answer.
We have got the distance between the earth and sun. The distance is,
$\Rightarrow 149597870700m$
We can rearrange the decimal terms we get,
$\Rightarrow 1.49\times {10}^{11}m$
The above value is approximately equal to$1.5\times {10}^{11}m$.

As mentioned, the value of $1AU$ is given as,
$\Rightarrow 1AU=1.5\times {10}^{11}m$
We can rewrite the given equation by bringing the $AU$to the right hand side and $1.5\times {10}^{11}m$ to the left hand side.
$\Rightarrow 1.5\times {10}^{11}m=1AU$
In the question they mentioned to calculate the number of astronomical units in one metre.
To measure the$1m$, we can divide the values like,
$\Rightarrow 1m={\displaystyle \frac{1}{1.5\times {10}^{11}m}}$
We can use the division method to simplify the given equation. We get,
$\Rightarrow 1m={\displaystyle \frac{1}{1.5\times {10}^{11}m}}$
$\Rightarrow 1m=0.666666667$

Now we can consider the power term. The power is given in the denominator. When we bring the power to the numerator, we get minus in the power term. That is,
$\Rightarrow 1m=0.666666667\times {10}^{-11}$
We can rearrange the decimal point, we get,
$\Rightarrow 1m=6.6666\times {10}^{-12}$
The above value is approximately equal to $6.67\times {10}^{-12}$.
$\therefore 1m=6.67\times {10}^{-12}AU$.

Hence, the correct answer is option (B).

Note: We should not get confused between the astronomical unit and light years that is used to measure the distance. The sunlight approximately takes $500$ seconds to reach the earth. That is to travel a distance of $1AU$ it approximately takes $500$ seconds.