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Decimal Addition (up to 2 decimal places)

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

When working with whole numbers, the far right 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. 

But, when you work with non-whole numbers that include decimals, numbers can stretch infinitely (or not) to the right. If your addition 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:





By lining the digits up by the right-most digit (the ones digit), all of the digits line up perfectly.  There is a ones column, a tens column, and a hundreds column, and they are all aligned.But, when you work with numbers with decimals and line the numbers up by the right-most digit, the place values get messed up.  2, a one, is lined up with .5, a tenth.  And 3, a ten, is lined up with 1, which is a hundred.  If you add these numbers, in these columns, your answer will be completely wrong.


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

$$\eqalign{2&\\+34&.5\\+198&\\\hline\text{ }}$$

Sometimes it's easier to do this when you add a decimal to every number


And, in case you're wondering why you don't have to line whole numbers up by the decimal, you actually do.  Every time you write a whole number, there's an invisible decimal at the end.  We just don't always write it out (we know it's there).  Technically, you could write the whole number problem like this:


But, we typically drop the decimal point and the zero when we know we're dealing with whole numbers (why write more than you have to?)

So, basically, when adding decimals: take your numbers, line them up vertically by the decimal (add the decimal to the end of whole numbers if it helps) and add normally! Then bring the decimal down into your answer. 

Practice Problems: