Question

What is the ratio of Milky Way radius to our solar system radius given that the distance from Pluto to sun is $5.9\times {10}^{12}$ metres and the milky way disk radius is $3.9\times {10}^{20}$ metres? Round off coefficient to the nearest tenth.$$$$

Answer 1

Hint: The ratio is the dimensionless quantity and it is the relationship between the two quantities as the quotient of one divided by the other. It is simply the comparison between the two same kinds of the quantities. Generally it is expressed in the form of the fraction.

Complete step-by-step answer:
Given that- the distance from Pluto to sun is $5.9\times {10}^{12}$ metres
Since, Pluto is the farthest planet.
Hence, the radius of Solar system is $=5.9\times {10}^{12}$
Radius of the Milky Way is $=3.9\times {10}^{20}$ metres
Therefore, the ratio of the Milky Way radius to our solar system radius is
$={\displaystyle \frac{3.9\times {10}^{20}}{5.9\times {10}^{12}}}$
By the quotient rule – to divide the two exponents with the same base, keep the base and subtract the powers.
$\Rightarrow$ This is just like reducing the fractions. ${\displaystyle \frac{a^m}{a^n}}=a^{m-n}$
$\begin{array}{rl}& ={\displaystyle \frac{3.9\times {10}^{20-12}}{5.9}}\\ & ={\displaystyle \frac{3.9\times {10}^8}{5.9}}\end{array}$
Simplify using basic mathematical operations
$\begin{array}{rl}& ={\displaystyle \frac{39\times {10}^8}{59}}\\ & ={\displaystyle \frac{390\times {10}^7}{59}}\\ & =6.61\times {10}^7\end{array}$
The required answer - $6.6\times {10}^7$ is the ratio of Milky Way radius to our solar system radius given that the distance from Pluto to sun is $5.9\times {10}^{12}$ metres and the Milky Way disk radius is $3.9\times {10}^{20}$ metres.

Note: Always check the units of the given terms and change all the units of the quantities to the same unit. Write the given quantities in the ratio as a fraction. The ratio can also be expressed as a decimal or the percentage. The words such as proportion, rate, relationship, relation are all the same and are the synonym for the word “ratio”.