Decimal Subtraction (1-2 decimal places)

The process of subtracting numbers with decimals is exactly the same as the process of subtracting whole numbers. The only difference is in the set-up.

When working with whole numbers, the right-most digit of every number you deal with is a ones digit, so as long as you line up numbers along the right side, all of the place values line up.

When you work with decimals, numbers can stretch infinitely (or not) to the right. If your subtraction problem contains even a single number with a decimal, you can no longer line the numbers up by the right-most digit. You must line numbers up by the decimal point.  

Look at the difference between the two problems below:

$$\require{cancel}\eqalign{198-34=\\\\198&\\-34&\\\hline234}$$

 

$$\eqalign{198-34.6=\\\\198&\\-34.6&\\\hline???}$$

 

By lining the digits up by the right-most digit (the ones digit) the numbers on the left all line up perfectly.  There is a ones column, a tens column, and a hundreds column.But, when you line up numbers with decimas by the right-most digit, the place values get messed up.  8, a one, is lined up with .5, a tenth. And 3, a ten, is lined up with 1, which is a hundred.  If you subtract these numbers in these columns, your answer will be completely wrong.  In fact, it would be negative, and we know that $198-34.5$ is not negative!

You have to line these numbers up by their decimal points:  

$$\eqalign{198&\\-34&.6\\\hline\text{ }}$$

And, because in subtraction, it's so easy to forget to borrow, we recommend putting decimals after whole numbers and filling in empty place values with zeros so that both numbers in the subtraction problem extend the same number of places to the right. 

$$\eqalign{198&.0\\-34&.6\\\hline \text{}}$$

With the extra zeros in place, students are less tempted to make the most common decimal subtraction error: forgetting to borrow (without a zero on top, it's just so easy to bring that bottom number down!):

$$\eqalign{19\cancel{8}\!&.\!\!^10\\-34&.6\\\hline163&.4}$$

So, basically, when subtracting decimals: take your numbers, line them up vertically by the decimal (add the decimal to the end of whole numbers if it helps) and subtract normally!  

If you feel like you need a little more explanation on this subject, review the lesson on Decimal Addition -- we go into more detail there!

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