Question

How do you write $9,300,000,000$ in scientific notation?

Answer 1

Hint: The scientific notation of a number is expressed as $a\times {{10}^{b}}$ where a is a number greater than or equal to one and less than ten, and b is any integer. Therefore, we need to shift the decimal point of the given number such that there is only a single digit left at its left. This can be done by dividing and multiplying the given number by ${{10}^{9}}$. After this, we will finally obtain the scientific notation for the given number.

Complete step by step answer:
We know that the scientific notation of a number is expressed as $a\times {{10}^{b}}$ where a is a number greater than or equal to one and less than ten, and b is any integer.
Now, according to the question, the given number is equal to $9,300,000,000$ which has to be written in the form of the scientific notation. According to the general form of the scientific notation, the number multiplied with ten raised to some power must have only a single digit to the left of the decimal point. According to the given number, which is equal to $9,300,000,000$, this number would be equal to $9.3$. Therefore, we multiply and divide the given number by ${{10}^{9}}$ to get
$\begin{align}
  & \Rightarrow \dfrac{9,300,000,000}{{{10}^{9}}}\times {{10}^{9}} \\
 & \Rightarrow 9.3\times {{10}^{9}} \\
\end{align}$

Hence, we have finally written the given number in the form of the scientific notation as $9.3\times {{10}^{9}}$.

Note: Writing a number in the form of the scientific notation does not change its value. We change only the form of the representation of the given number such that it gets represented in a more convenient manner. Also, we can note that the power over ten, equal to nine, is just equal to one less than the number of digits in the given number, which is equal to ten.