Adding decimals

Adding decimals is very similar to adding whole numbers. However you must remember that when adding decimals, you must line up the decimal points vertically. This means that if you are adding two decimals, you must write them so that the decimal point of the second number is directly under the decimal point of the first. Look at the examples below.

Example 1:

12.25 + 5.64 

Step 1: Make sure decimal points are lined up vertically as shown below.

Step 2: Add as you normally would add whole numbers. Ensure that you put a decimal point in your answer. It must be directly under the other decimal points as seen below.

Example 2: 

Find the sum of 41.42 and 5.3

Step 1: Line up the decimal points vertically as shown below.

In this case it may look a little strange as the second number does not have a digit in the hundredths place. However it is correct as the decimal points are lined up vertically.

Step 2: Add as normal. Note that you can add a zero in the hundredths place as seen below. It does not change the value of the number (5.3 = 5.30).

Example 3 (Adding a whole number and a decimal)

53.91 + 34

Step 1: We can rewrite 34 as a decimal by adding a decimal point followed by one or more zeros. It does not change the value of the number. The number 34 is equal to 34.0 or 34.00. After writing 34 as a decimal, line up the decimal points vertically as seen below.

Step 2: Add as you normally would. Remember that the decimal point in your answer must be placed directly under the other decimal points.

Example 4 (Adding decimals with regrouping)

What is the sum of 327.84 and 51.43?

Step 1: Line up the decimal points vertically as shown below.
Step 2: Add the same way you would normally add whole numbers. Note that the digits in the tenths column will add up to a two digit number. Look at the working below.

Note that the numbers in the tenths column add up to 12. The 2 is placed in the same column (the tenths column) and the 1 is moved over to the next column (the ones column). This is just like what we do when adding whole numbers. Always remember to place the decimal point in your answer directly below the other decimal points.