Question

How do you write \[8.2\times {{10}^{-2}}\] in standard form?

Answer 1

Hint: We are given a number which is in scientific notation form and we are asked to write it in standard form. Usually, the terms standard form and scientific notation form are used interchangeably, in that case it is already in standard form. Else, if it means the normal or the general form then, according to the power on 10, which is negative, we will shift the decimal place to the left of \[8.2\] by two places and we will have the answer.

Complete step by step answer:
According to the question given to us, we have the number given to us in scientific notation. We are asked to write this number in the standard form.
Scientific notation, which we use often while dealing with large numbers is also called the standard form. In that case, the given number is already in the standard form.
If the question meant to write the given number in the normal form then, we have to decimal point to the original position.
We can see that the power raised to 10 is \[-2\]. Since it is negative, we will shift the decimal point to the left of the number by two places. So, we have,
\[8.2\times {{10}^{-2}}\]
\[\Rightarrow \dfrac{8.2}{{{10}^{2}}}=\dfrac{8.2}{100}\]
\[\Rightarrow 0.082\]
Therefore, \[8.2\times {{10}^{-2}}=0.082\].

Note:
Read the question carefully to understand what exactly the question is asking us to find. Also, while shifting the decimal places, make sure if the charge of the power to which 10 is raised to is positive, the decimal point will shift towards the right and if the charge is negative, the decimal point will shift towards the left.