Comparing decimals
In a nutshell
Being able to compare the sizes of different decimals allows them to be placed in order. A number line can be useful to help visualise this process.
Which is bigger?
In order to decide which number is larger, its placement and position on a number line can be looked at. The further up the number line it is, the bigger its size.
Example 1
Which is bigger: $4.2$ or $4.7$?
$\begin{array}{cccccccccccccc}&&&& \\& &&&\downarrow &&&&&&&&&&\downarrow &&&&\\\bold4&&4.1&&\underline{4.2}&&4.3&&4.4&&4.5&&4.6&&\underline{4.7}&&4.8 &&4.9&&\bold5\\&&&&&&&&&&&&&&&&&&&& \\ \hline\end{array}$
Notice how $4.7$ is positioned further up the number line than $4.2$.
What's more, $4.2$ and $4.7$ both share the same digit in their ones column whilst the digits in the tenths column differ.
$7$ is greater than $2$ and so:
$4.7$ is greater than $4.2$.
Ordering decimals
To order a set of decimals, compare them with each other and decide which are bigger.
Procedure
1.
 Look at the digits in each place value column, one at a time from left to right.

2.
  If the digits are the same, move on to the next place value column.
 If the digits are different, place them (and the number associated with them) in order the required order.

3.
 Continue the process until all the decimals are arranged in order.

Example 2
Place the numbers $1.72, 2.52, 1.68$ and $1.73$ in order from smallest to largest.
Look at the digits in the ones column: $1,2,1$ and $1$.
$2$ is the only differing digit. It is bigger than $1$, so $2.52$ is the largest number.
Look at the remaining digits in the tenths column: $7,6$ and $7.$
$6$ is the only differing digit. It is smaller than $7$, so $1.68$ is less than $1.72$ and $1.73$.
Look at the remaining digits in the hundredths column: $2$ and $3$.
$3$ is bigger than $2$ so $1.73$ is greater than $1.72$.
Using the information gathered, place all four numbers in order.
$\underline{1.68,1.72,1.73,2.52}$