📖Definition
Usually a number is made up of one or more digits and possibly a decimal point. Where these digits are placed indicates the value they represent.
For example, 32145 24.513 1.2345 are all written using the digits 1, 2, 3, 4, 5 but are very different in size.
Method
If there is no decimal point in a given number, the rightmost digit represents the units and as we move left by one digit, the value it represents is 10 times more than the one to its right. So, in the case of 32145, the 5 represents units, the 4, tens, the 1, hundreds and so on.
When there is a decimal point, the digit to the right of it represents tenths and then as we move right by one digit, the value it represents is 10 times less than the digit to its left. So, in the case of 24.513, the 5 represents 10ths, the 1, 100ths and the 3, 1000ths.
Below shows what each digit in the number 5791.438 represents.
Diagram
Sometimes you might be asked to work out the value of a point on a Number Line.
Diagram
The first step is to work out how much each step on the number line represents.
To get from the -0.02 at the left to the 0.03 at the right requires 5 steps.
The difference between 0.03 and -0.02 = 0.03 - (-0.02) = 0.05
So, each step represents 0.05/5 = 0.01.
Now we can work out that the arrow is pointing half way between 0.01 and 0.02 ie. at 0.015
💡Tips/hints
When placing a given set of numbers in order, it can help to add decimal points if they don't have them and then write them in a column aligning the decimals points and making sure the units, tens, hundreds etc line up as well as the decimal parts.
Diagram
The digits representing the biggest numbers are at the left, so start from the left and stop at the first column with one or more digits in it. Here the first column is the 10s and there's just one digit in there, the tens digit from 10.01. So, 10.01 is the largest of the numbers.
Now let's find the next largest. Move right one to the units column.
The four remaining numbers each have a digit in that column.
There are two highest ones this time, both 9s.
So, we need to look to the next column to see which number is higher.
Step past the decimal point and the two digits in the next column are 0 and 2.
2 is higher so, 9.215 is the next highest number, and 9.09 the one after that.
Go back to the units column where we still have two digits to check.
1 is higher than 0, so the next highest number is 1.89 and the smallest number is 0.98
✏️Example
Put the numbers: 5.778, 0.678, 6.05, 0.877, 5.9 in order from smallest to largest.
✅Solution
First write them in a grid and work out the order from largest to smallest as outlined above.
Then, as we're asked for smallest to largest, reverse the order.
Your answer should be: 0.678, 0.877, 5.778, 5.9, 6.05