Question

How do you write the given number 54.08 in scientific notation?

Answer 1

Hint: We start solving the problem by recalling the definition of scientific notation as the way of expressing number that are too large or too small to be conveniently written in decimal form such that the numbers are to be written in the form $m\times {{10}^{n}}$, where ‘m’ should be written in such a form that there is only digit present in it before the start of the decimals. We then write the given number in the scientific notation by following all the points of this definition.

Complete step by step answer:
According to the problem, we need to write the given number 54.08 in the scientific form.
Let us recall the way of expressing numbers in scientific notation.
We know that the scientific notation is the way of expressing numbers that are too large or too small to be conveniently written in decimal form. In scientific notation the numbers are to be written in the form $m\times {{10}^{n}}$. Here ‘m’ should be written in such a form that there is only a digit present in it before the start of the decimals.
So, we need to convert the number 54.08 in the form of $m\times {{10}^{n}}$ which is as follows:
$\Rightarrow 54.08=5.408\times {{10}^{1}}$.
$\therefore $ The scientific notation of the number 54.08 is $5.408\times {{10}^{1}}$.

Note:
We should know that the power of 10 indicates the number of placeholders present, which means that the number of times that the given number is divided by 10 or multiplied by 10. We should not write the scientific notation of the given number 54.08 as $540.8\times {{10}^{-1}}$ instead of $5.408\times {{10}^{1}}$, which is the most common mistake done by students. Similarly, we can expect the problems to express the number 0.00835 in scientific notation.