Adding Decimals

Example 1: Add: 52.3 + 973.41

Analysis: Let's use our knowledge of mixed numbers to help us analyze this problem.

52.3 = 52_and_3tenths.gif and  973.41=973_and_41hundredths.gif

Recall that a decimal number can have a whole-number part and a fractional part. When adding decimals, you must first line up all the decimal points in a column. Lining up the decimal points ensures that each digit is in the proper place-value position. Once each digit is in the proper place-value position, the whole-number parts are lined up with each other, and the fractional parts are lined up with each other. This is shown in the table below.

PLACE VALUE AND DECIMALS
millions.gif   hundred_thousands_0.gif  ten_thousands_0.gif thousands.gif  hundreds_0.gif  tens_0.gif  ones_0.gif and_gg_0.gif  tenths_0.gif hundredths_0.gif  thousandths_0.gif ten_thousandths_0.gif   hundred_thousandths_0.gif millionths_0.gif
          5 2 . 3          
        9 7 3 . 4 1        
----------- Whole-Number Part -----------   ---------- Fractional Part -----------

Now that we have lined up the decimal points, you will notice that the numbers being added do not have the same number of decimal digits. Let's look at this problem on paper without a place-value chart.

      52.3

+  973.41

You can write an extra zero to the right of the last digit of the first decimal so that both decimals have the same number of decimal digits.

      52.30

+  973.41

Just as with whole numbers, start on the right, and add each column in turn. Note that you are adding digits in the same place-value position.

      52.30

+  973.41
  1025.71

Place the decimal point in the sum.

      52.30

+  973.41
  1025.71

Answer: The sum of 52.3 and 973.41 is 1025.71.

Example 2: Add: 0.078 + 3.09 + 0.6

    0.078

    3.090

+  0.600

Analysis: If you need to carry (i.e. if a columns adds up to more than 9), remember to add the tens digit of that column to the next column.

       1

    0.078

    3.090

+  0.600
    3.768

Answer: The sum of 0.078 and 3.09 and 0.6 is 3.768.

Dollars CentsExample 3: Add: $77.23 and $88

Analysis: Each of these numbers represents money; however, the second is written as a whole number. Change the second number so that it has two decimal digits, and then perform the addition.

   $  77.23

+ $  88.00
   $165.23

Answer: The sum of $77.23 and $88 is $165.23.

DecimalsProcedure: To add decimals, follow these steps:

  1. Line up all the decimal points in a column.
  2. When needed, write one or more extra zeros to the right so that both decimals have the same number of decimal digits.
  3. Start on the right, and add each column in turn. (Add digits in the same place-value position.)
  4. If you need to carry, remember to add the tens digit of that column to the next column.
  5. Place the decimal point in the sum.

Example 4: Add: 28.5 + 34.5

Analysis: You will need to carry more than once. Accordingly, the addition will be divided into three steps to show the process of carrying.

     1                   1 1               1 1
   28.5               28.5             28.5
+ 34.5            + 34.5          + 34.5
       .0   arrow_right_0.gif        3.0   arrow_right_0.gif      63.0

Answer: The sum of 28.5 and 34.5 is 63.

Example 5: Add: 3.986 + 37 + 25.902

     1                     1 1                   1 1
     3.986                3.986             3.986
   37.000               37.000           37.000
+ 25.902            + 25.902         +25.902
       .888   arrow_right_0.gif        6.888 arrow_right_0.gif     66.888

Answer: The sum of 28.5 and 34.5 is 66.888.

Example 6: Add: $12.95 + $67.89 + $54.55

             1                   2  1               1  2  1
   $  12.95          $  12.95          $  12.95
   $  67.89          $  67.89          $  67.89
+ $  54.55       + $  54.55      +  $  54.55
   .39   arrow_right_0.gif         $    5.39   arrow_right_0.gif  $135.39

Answer: The sum of $12.95 and $67.89 and $54.55 is $135.39.

DimeExample 7: A dime rolled 5.8794 cm and then rolled 7.48 cm. How far did it roll altogether?

      1                     1  1                  1 1  1
   5.8794               5.8794             5.8794
+ 7.4800            + 7.4800          + 7.4800
     .3594   arrow_right_0.gif       3.3594   arrow_right_0.gif   13.3594

Answer: The sum of 5.8794 cm and 7.48 cm is 13.3594 cm.

Summary: When adding decimals, you must first line up all the decimal points in a column. Lining up the decimal points ensures that each digit is in the proper place-value position. You can then add digits in the same place-value position to find the sum.


Exercises

Directions: Read each question below. You may use paper and pencil to help you add. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. Add:  46.907 + 2.0184
ANSWER BOX:   

RESULTS BOX: 

2. Add: 504.6 + 13.7 + 0.029
ANSWER BOX:   

RESULTS BOX: 

3. Add: $234.50 + $187.95
ANSWER BOX: $  

RESULTS BOX: 

4. Add: 15.419 + 0.3 + 297.0651
ANSWER BOX:   

RESULTS BOX: 

5. Jill bought two sweaters for $19.99 each and a pair of jeans for $27. How much did she pay altogether (assuming there was no sales tax)?
ANSWER BOX: $  

RESULTS BOX: