Question

How do you rewrite the number in scientific notation $0.00003$?

Answer 1

Hint: We first explain the purpose of scientific notation. Then we explain the process. We use the decimal point and move it rightwards to multiply the new number with $\dfrac{1}{10}$ equal to ${{10}^{-1}}$. The multiplied form is the scientific form of the given number.

Complete step by step answer:
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
For the given number we move the decimal to the right one position. The decimal goes to the very end of the number. The more we move to the right, the more we multiply with ${{10}^{-1}}$.
We explain the first two steps. The decimal starts from its actual position in $0.00003$.
Now it crosses one zero in $0.00003$ which means we have to multiply $\dfrac{1}{10}$. There are four more digits after decimal. We compensate by multiplying ${{10}^{-1}}$.
So, $0.00003$ becomes \[0.0003\times {{10}^{-1}}\].
Now in the second step the point crosses two zeroes in total which gives \[0.003\times {{10}^{-2}}\].
We again compensate by multiplying ${{10}^{-1}}$.
We go on like this till the decimal point has reached the rightmost position of the number.
In $0.00003$, the movement of the decimal point happens 5 times which means \[3\times {{10}^{-5}}\].

Therefore, the scientific notation of $0.00003$ is \[3\times {{10}^{-5}}\].

Note: We also can add the zeros after decimal points and make the notation as \[3\times {{10}^{-5}}\] for the simplicity and mathematical use. The use of zeroes is unnecessary. But in cases where we have digits other than 0 after decimal, we can’t ignore those digits.