Question

How do you write $ 0.0006730 $ in scientific notation?

Answer 1

Hint: The purpose of scientific notation was developed in order to easily represent numbers that are either very large or very small. We use the decimal point and move it rightwards. To compensate for that we have to multiply the new number with $ \dfrac{1}{10} $. 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 point where we have crossed one non-zero number. We compensate for the movement of the decimal by multiplying $ \dfrac{1}{10} $ to the main number $ 0.0006730 $. This fraction is equal to $ 0.1 $.
We explain the first two steps. The decimal starts from its actual position in $ 0.000673 $.
Now it crosses one zero. The number changes from $ 0.000673 $ to $ 0.00673 $ . This means we have to multiply \[{{10}^{-1}}\]. There are five digits after the decimal.
So, $ 0.000673 $ becomes \[0.00673\times {{10}^{-1}}\].
Now in the second step the point crosses two zeroes in total. The number again changes from $ 0.00673 $ to $ 0.0673 $ . This gives \[0.0673\times {{10}^{-2}}\]. We again multiplied \[{{10}^{-1}}\] for the decimal’s movement.
We go on like this till the decimal point has reached the right-side position of the digit 6.
To reach that position the movement of the decimal point happens 2 more times which means \[6.73\times {{10}^{-4}}\].
Therefore, the scientific notation of $ 0.0006730 $ is \[6.73\times {{10}^{-4}}\].

Note:
 We deliberately omitted the zero which was at the rightmost position after decimal as it has no use after decimal if it’s not being followed by a non-zero digit. We can form the notation as \[673\times {{10}^{-6}}\] but that’s not scientific. 673 becomes a large number. Scientific notation helps in the case of non-terminating decimals.