Small Numbers

In certain scientific subjects such as, for example, biology and chemistry, there are extremely large or infinitesimally small numbers.
For example:
The mass of planet Earth is $6,000,000,000,000,000,000,000,000$ kg.
    or
The radius of a carbon atom is $0.000,000,000,07$ m.
To express these numbers in a simple and practical way, without having to write a lot of digits, we can use powers.

Scientific notation is a system for expressing very large or very small numbers in a practical way.
According to scientific notation, the number will be represented as the product of a certain number between $1$ and $10$ multiplied by $10$ raised to some power.
That is:

$m \times 10^e$

$m$ will be a number between $0$ and $1$
If $e$ is a positive integer, the whole expression will be some number greater than $1$
If $e$ is a negative integer, the whole expression will be some number less than $1$

Let's remember that, when we have a decimal number like, for example:
$5.32$
and we move the decimal point one step to the right, we are actually multiplying the number by $10$.
That is, if we multiply
$5.32$
by $10$
We will get:
$53.2$
Similarly, if we move the decimal point one step to the left, we are actually dividing the number by $10$.

To write large and small numbers in a practical way we will use the powers of $10$.
You'll catch on right away.
Let's take an example of a number that is not too large: $183$
If we move our imaginary decimal point one step to the left, we are actually dividing the number by $10$.
Therefore, to not alter the numerical value we must immediately multiply it by $10$.
That is:

$183=18.3 \times 10$

If we move the point another step back, we must multiply by $100$.
That is:
$183=18.3 \times 10=1.83 \times 100$
We know that, $100$ can be written as $10^2$
Therefore, we can express $183$ as: $1.83 \times 10^2$
Similarly, if we take a larger number, for example: $5,000,000$
We can say it is equivalent to:
$5 \times 1,000,000$
We know that, $1,000,000$ is equivalent to $10^6$
Therefore:
$5,000,000=5 \times 1,000,000=5 \times 10^6$
So how can we write numbers using scientific notation without getting confused?

Steps for the notation of very large numbers according to scientific notation:

1. We will move the decimal point to the right until it is placed after a number that is less than $10$.
2. We will count how many steps we have moved the decimal point to the right. The number of steps taken will be the exponent of $10$, only this time, in negative.
3. We will multiply the $10$ raised to the power we found (in negative) by our number $-m$ and that will give us the scientific notation.

Let's take the following number as an example:
$0.00654$

We moved the decimal point to the right until it was behind a number greater than $0$.
We counted the number of steps taken and got $3$. Since we moved the decimal point to the right, the exponent will be the number of steps taken in negative, that is $-3$.

Therefore, we will obtain:
$6.54 \times 10^{-3}$