3.4 The Correct Order
In the last section, we compared numbers on the number line. This is a good way to compare decimal numbers. It always works to draw things out but it can be difficult to to this every time you want to decide which of two numbers is greater. There is another better way to decide which of two numbers is the greater.
Example A
We take the numbers from the last section and compare 0.05 with 0.2.
0.05 
= 
0 wholes 
0 tenths 
5
hundredths 
0.2 
= 
0 wholes 
2 tenths 

In order to decide which number is the greatest, we look first at the part with the whole number. Both have 0 whole numbers, and we then instead look at the tenths part. 0.05 has 0 tenths and 2 has 2 tenths. That 0.05 has 5 hundredths and 0.2 has 2 hundredths doesn’t matter because the tenths has already determined that 0.2 is greater. Then we can now determine that:
0.2 
> 
0.05 
If you look at the picture, it becomes even clearer:



0.2 
> 

0.05 
Example B
Which of the numbers 0.612 and 0.62 is greatest?
0.612 
= 
0 whole 
6 tenths 
1 hundredths 
2 thousandths 
0.62 
= 
0 whole 
6 tenths 
2 hundredths 

Both the numbers have 0 wholes and 6 tenths, and at this point, we can’t determine which of them is the greatest. 0.612 has only 1 hundredths and 0.62 has 2 hundredths though. Now we can determine that:
0.62 > 0.612
That 0.612 then has 2 thousandths no longer matters. It is still less than 0.62.
We can even see this in pictures:

0.612 



0.62 


In order to determine which of the two decimal numbers is the greatest, do the following:
1. Compare the whole numbers.
2.
If the whole numbers are equal, compare the tenths
3.
If the tenths are equal, compare the hundredths
4.
If the hundredths are equal, compare the thousandths
5.
And so forth. 