Question

How do you write $0.00000017$ in scientific notation?

Answer 1

Hint: In the scientific notation, a too big or a too small number is conveniently written in the form of $N\times {{10}^{m}}$. Here $N$ is a number greater than or equal to one and less than ten. So the range of $N$ is $1\le N<10$. And $m$ is an integer which represents the exponent of ten. For converting the given number $0.00000017$ into the scientific notation we have to consecutively multiply it by ten until it becomes equal to $1.7$.

Complete step by step answer:
The number given to us in the question is $0.00000017$. Let us represent this number as
$n=0.00000017.......(i)$
Now, we know that the scientific notation is a method of representing a number, which is either too small or too large, conveniently in the form of a decimal number between one and ten, and multiplies by ten raised to some power. So, the general form of the scientific notation is $N\times {{10}^{m}}$. Here $N$ is called the significand, while $m$ is called the order of the magnitude.
So, for converting the given number into the scientific notation, we multiply both sides of the equation (i) by ${{10}^{7}}$ to get
$\begin{align}
  & \Rightarrow {{10}^{7}}n=0.00000017\times {{10}^{7}} \\
 & \Rightarrow {{10}^{7}}n=1.7 \\
\end{align}$
Finally, dividing both sides of the above equation by ${{10}^{7}}$, we get
$\begin{align}
  & \Rightarrow \dfrac{{{10}^{7}}n}{{{10}^{7}}}=\dfrac{1.7}{{{10}^{7}}} \\
 & \Rightarrow n=1.7\times {{10}^{-7}} \\
\end{align}$

Hence, the required scientific notation of the number $0.00000017$ is $1.7\times {{10}^{-7}}$.

Note: If a number given is less than one, then we can easily write the number in the scientific notation. We just have to count the number of zeroes from the left until we encounter a non-zero digit. The order of the magnitude will be equal to the negative of the number of zeros counted. Like in this case, the number of zeroes before the first non-zero digit $\left( 1 \right)$ is equal to $7$. Hence, the order of magnitude is equal to $-7$.