Question

How can one write the scientific notation of a negative number?

Answer 1

Hint: Scientific notation of a number is the representation of numbers in such a way that very large numbers can be read easily without any discrepancy. Also in scientific notation the numbers are represented in the form $p \times {10^n}$where $p$should be between 1 and 10 i.e. \[1 \leqslant p \prec 10\]and $n$is an integer.
We can solve this question by using the above-stated definition of scientific notation.

Complete step by step answer:
Given
Any negative number has to be written in scientific notation.
So by the basic definition of scientific notation, the numbers are represented in the form $p \times {10^n}$
where \[1 \leqslant p \prec 10\]and $n$is an integer. (Positive numbers)
Also in the case of negative numbers, the same rules apply except after putting the number in scientific notation in addition they have a negative sign by the leading number.
i.e. it’s represented in the form $ - \left( {p \times {{10}^n}} \right)$where \[1 \leqslant p \prec 10\]and $n$is an integer.
Let’s take an example for more clarity:
Scientific Notation of$ - \left( {345.777} \right)$:
As mentioned above doing the following steps;
$
   \Rightarrow - \left( {345.777} \right) = - \left( {3.45777 \times {{10}^2}} \right) \\
   \Rightarrow - \left( {345.777} \right) = - 3.45777 \times {10^2} \\
 $
So for negative numbers, scientific notation is written as described above and has in addition only a negative sign compared to the standard form.

Note:
To convert the general format negative numbers to scientific notation form certain rules have to be followed as given below:
1. The position of the decimal point should be such that there is only a single digit before it.
2. While moving the decimal points one should take care of the position which has been moved since it determines the power of 10.
3. Also the direction to which the decimal point has been moved is to be noted, if it has been moved to the left then the power is positive and if it’s moved to the right then the power is negative.
4. After performing all these steps put a negative sign by the leading number.