Question

How do you express $0.00000804$ in scientific notation?

Answer 1

Hint: The scientific notation of any number is written in the form of $a\times {{10}^{m}}$, where $a$ is a number greater than or equal to one and is less than one, and $m$ is an integer. For writing the given number, which is written as $0.00000804$, in the scientific notation, we need to multiply it by ten repeatedly till it becomes equal to a number greater than or equal to one, and less than ten, which is equal to $8.04$ in the case of the given number.

Complete step-by-step answer:
Let us consider the number given in the above question as
$\Rightarrow n=0.00000804$
We know that in scientific notation, we write a number in the standard form of $a\times {{10}^{m}}$, where $a$ is a number greater than or equal to one and is less than one, and $m$ is an integer. Therefore, for writing the given number in the scientific notation, we multiply the above equation by ${{10}^{6}}$ to get
\[\begin{align}
  & \Rightarrow {{10}^{6}}n=0.00000804\times {{10}^{6}} \\
 & \Rightarrow {{10}^{6}}n=8.04 \\
\end{align}\]
On dividing the above equation by \[{{10}^{6}}\], we get
\[\begin{align}
  & \Rightarrow \dfrac{{{10}^{6}}n}{{{10}^{6}}}=\dfrac{8.04}{{{10}^{6}}} \\
 & \Rightarrow n=\dfrac{8.04}{{{10}^{6}}} \\
\end{align}\]
Finally, using the rule of the negative exponents, we can write the above equation as
\[\Rightarrow n=8.04\times {{10}^{-6}}\]
Hence, we obtained the scientific notation of the given number as \[8.04\times {{10}^{-6}}\].

Note: For writing the numbers of these types in the scientific notation, which are less than one, we can also count the number of zeroes before the first non-zero digit in the given number. For example in the given number $0.00000804$, the number of zeroes before the first non-zero digit, which is equal to $8$, is equal to six. The negative of this number will be equal to the power over ten in the scientific notation of the number.