Density

The density of decimal numbers is a topic that immediately relates to the comparison of decimal numbers.
In reality, there's nothing new about this topic, so, if you know how to compare decimal numbers without difficulty, you'll understand it perfectly.

What should we know?
Density symbolizes (not surprisingly) how dense decimal numbers are.
Let's look at it on the number line to understand it better:

Between two numbers, it's very simple to say that their halves are there. But that's not all, we already know that between $1$ and $1.5$ there are more numbers, right?
Let's see it this way:

This time we've added the tenths.
But hey, these are not all the numbers that are here between $1$ and $1.5$.
If we add the hundredths (for example, between $1.1$ and $1.2$ we'll see many other numbers...)

Observe:

We added the hundredths and saw the numbers between $1$ and $1.2$.
We suppose you already understand what will happen now....
Also, between $1.01$ and $1.02$ there are infinite numbers that we could see just by adding the thousandths on the number line.
Look at it:

What does this tell us?
That numbers are so dense that, between each pair of numbers, there is another infinity of numbers and that, to notice them, we only need to look at the tenths, hundredths, and thousandths.