Question

How do you write $0.00007$ in scientific notation?

Answer 1

Hint: In this question, we have to convert a decimal notation into scientific notation. As we know, a decimal notation is a number that has a decimal point, which means the decimal can be removed by placing the numbers after the decimal in the denominator. Also, a scientific notation is either a very large number or a small number; it is represented when a number lies between 1 to 10 is multiplied by a power, which implies $a\times {{10}^{b}}$ where a is the number between 1 and 10 and b is either negative for small numbers. So, in this problem, we first count the total numbers of 0 after a decimal point that is where the number 7 appeared, and then write it in the form of scientific notation, which is our required solution to the problem.

Complete step-by-step solution:
According to the question, we have to find the scientific notation from a decimal notation.
The decimal notation given to us is $0.00007$ -------- (1)
So, we first count the total number of zeros after the decimal point, we have
$\begin{align}
  & \text{ }0.00007 \\
  & \text{ }\uparrow \uparrow \uparrow \uparrow \\
\end{align}$
So, we get 4 zeroes after a decimal point and before 7.
Also, we have to count the decimal point as a zero; therefore in total, we get 5 zeroes before a decimal point, thus we get the value of b for a scientific notation is,
$b=-5$
Therefore, we can write it as $7.0\times {{10}^{-5}}$
$7\times {{10}^{-5}}$ which is our required solution.
Therefore, for the decimal notation $0.00007$, its scientific notation is equal to $7\times {{10}^{-5}}$

Note: While solving this problem, keep in mind the difference between scientific notation and decimal notation. Also, a scientific notation is only represented for decimal numbers. Do not forget to count the decimal as 0.