Question

As of the year $2000$, the Earth’s population was estimated to be $6,200,000,000$. How do you write this number using scientific notation?

Answer 1

Hint: According to the above question, we have to write the Earth’s population, which is given to be equal to $6,200,000,000$, using the scientific notation. The scientific notation is generally expressed in the form of $a\times {{10}^{b}}$, where $a$ is a decimal number greater than or equal to one and less than ten, while $b$ is an integer which is an exponent over ten. So in order to convert the given number $6,200,000,000$ into the scientific notation, we have to divide it by ten until it becomes equal to $6.2$. The number of times this multiplication is carried out will be equal to the exponent over ten in its scientific notation.

Complete step by step solution:
The population of the Earth for the year $2000$ is given to be equal to $6,200,000,000$. We are asked to write this number using the scientific notation. We know that the scientific notation is expressed as $a\times {{10}^{b}}$, where $a$ is a decimal number greater than or equal to one and less than ten, while $b$ is an integer. Therefore, for writing the number $6,200,000,000$ using the scientific notation, we divide and multiply it by ${{10}^{9}}$ to get
\[\begin{align}
  & \Rightarrow 6,200,000,000\times \dfrac{{{10}^{9}}}{{{10}^{9}}} \\
 & \Rightarrow 6.2\times {{10}^{9}} \\
\end{align}\]
Hence, the number given in the above question is expressed in the scientific notation as \[6.2\times {{10}^{9}}\].

Note:
In the above question, we are given two numbers $2000$ and $6,200,000,000$. So we might get confused about which number is to be expressed in the scientific notation. For this we must use the fact that the scientific notation is used to express a number conveniently which is complicated in the decimal representation. Since it is clear that the number $6,200,000,000$ is appearing much complicated, it must be written in the scientific notation.