Question

How do you find out the mass of 6 billion dust particles, if a dust particle has a mass of $7.53\times {{10}^{-10}}g$?

Answer 1

Hint: We are given a question having the mass of a single dust particle and using that we have to find the value of the mass of 6 billion dust particles. We will use a unitary method to solve this question. As one dust particle weighs $7.53\times {{10}^{-10}}g$, so the mass of 6 billion dust particles would be $7.53\times {{10}^{-10}}g$ multiplied by 6 billion. And then we will have the mass of 6 billion dust particles.

Complete step by step solution:
According to the given question, we have been provided with the mass of a single dust particle, that is, $7.53\times {{10}^{-10}}g$. And using this value, we have to find the value of the mass of 6 billion dust particles. In order to solve it, we will use the unitary method.
Unitary method involves using the value of a single unit and using this value, the value of more than one unit is determined as per the requirement.
So we have, Mass of one dust particle = $7.53\times {{10}^{-10}}g$
Mass of 6 billion dust particles (\[6,000,000,000\] or \[6\times {{10}^{9}}\]) \[=(7.53\times {{10}^{-10}}g)\times (6\times {{10}^{9}})\]
\[=(7.53\times 6)\times ({{10}^{-10+9}})g\]
\[=45.18\times {{10}^{-1}}g\]
Therefore, the mass of a 6 billion dust particle is \[45.18\times {{10}^{-1}}g\].

Note:
The word ‘billion’ we used in the above solution is used in the international system of numbering. Billion can also be said to be the product of 1 million and 1 thousand.
Some of the commonly used quantities that we hear in our everyday life are:
\[1thousand=1000\] or \[{{10}^{3}}\]
\[1million=1,000,000\] or \[{{10}^{6}}\]
\[1billion=1,000,000,000\] or \[{{10}^{9}}\]
\[1trillion=1,000,000,000,000\] or \[{{10}^{12}}\]
Also, while calculating the mass of 6 billion dust particles, don’t forget to write 6 with the billion figure as then the entire question would get wrong.