Adding Decimals

Adding decimals means finding the sum of two or more decimal numbers. Although adding decimals is similar to the regular addition of whole numbers, there are certain rules that need to be followed while adding them. Let us learn more about adding decimals, their rules, along with examples.

How to Add Decimals?

Adding decimals is similar to the usual addition of whole numbers. We know that a decimal number is a number with a whole number part and a fractional part which is separated by a decimal point. However, this does not change the rules for the addition of decimal numbers. For this, we need to align the decimal numbers according to their place values one below the other, keeping the decimal point intact, and then add the numbers. We should remember that the decimal place value chart has some extra place values, like, the place value just after the decimal point is called tenths, followed by hundredths, thousandths and so on.

Rules for Adding Decimals

While adding decimals, we need to remember some rules that would be helpful and make the addition easier.

Align the decimal numbers in such a way that they are placed in the correct place according to their place values.
Always convert the decimal numbers to like decimals, wherever needed.
Add zeros in the places wherever the length of the decimal numbers is not the same.
Now, add the numbers and place the decimal point aligned with the given decimal points.

Adding Decimals with Different Decimal Places

Sometimes, the given numbers are different in their length, that is, they do not have an equal number of decimal digits after the decimal point. In such cases, we convert the given decimal numbers to like decimals by adding the required number of zeros to the right of the decimal. This is done to make the process of addition easier. Like decimals have an equal number of digits after the decimal, for example, 0.14 and 2.35 are like decimals, whereas, unlike decimals have different number of digits after the decimal, for example, 6.32 and 6.324 are unlike decimals. So, after the given decimals are changed to like decimals, they are added and the sum is obtained.

Adding Like Decimals

Example: Add: 2.53 + 1.14.

Solution:

If we observe the given decimals, we see that they are like decimals, so, we will place them in order and do the regular addition.

2.53
+1.14
3.67

Therefore, after adding the decimals, we get the sum as 3.67

Adding Unlike Decimals

Example: Add: 6.3 + 2.54

Solution: We can see that the given decimals are unlike, so we will convert them to like decimals by adding the required number of zeros. We will count the number of digits after the decimal point in both the numbers and identify the higher one in them. In this case, 6.3 has one digit after the decimal, and 2.54 has two digits after the decimal. So, will make it 6.30 so that it becomes of the same length as 2.54. Now, we will add the decimals numbers.

6.30

+2.54

8.84

Therefore, the sum of the given decimals is 8.84

Adding Decimals with Whole Numbers

Adding decimals with whole numbers is simple to understand. We place a decimal point after the whole number and add the required number of zeros so as to make both the addends of the same length. This is done in such a way that it aligns with the number of digits in the other number. In other words, we convert them to like decimals and then add them.

Example: Let us add 4 to 6.54

Solution:

Step 1: We can see that 4 is a whole number and 6.54 is a decimal number. So, let us make both the numbers of equal length.

Step 2: Since there are two digits after the decimal in 6.54, we will place a decimal after 4 and add two zeros after it so that it becomes a decimal number too.

Step 3: Now, we will add the numbers and the sum of the given numbers will be 10.54

Adding Decimals by Regrouping

Adding decimals by regrouping is similar to the regrouping that is done in the addition of whole numbers. Regrouping is also termed as carrying over. In addition, if the sum of the addends is greater than 9 in any of the columns, we regroup it by carrying over the extra digit to the preceding column. Let us understand how to add decimals by regrouping with the following example.

Example: Add 14.62 + 12.63

Let us see how to add the given decimals by regrouping.

Step 1: Align the given numbers according to their corresponding place value columns and change them to like decimals, if needed. Ensure that the decimal points are aligned with each other.
Step 2: Start adding digits in each column individually, starting from the right and move to the left in the same way as we do for whole numbers. Add the numbers given in the hundredths column (h). 2 + 3 = 5 and write 5 below the column.
Step 3: Move to the tenths column (t) and add 6 + 6 = 12. Now, we cannot place ’12’ in this column since we can write only one digit below each column, so we regroup the number 12. For this, we write 2 in this column and carry 1 to the preceding column, that is, the ones column (O). This 1 (carry-over) is added along with the numbers in the ones column. Remember to place the decimal point below the decimal point.
Step 4: Now, let us add the numbers under the ones column. Here, after the carry-over is placed in this column, it is added along with the other addends. This will be, 4 + 2 + 1 (carry-over) = 7.
Step 5: Finally, add the numbers given in the tens column (T), that is, 1 + 1 = 2.

Thus, the sum of the numbers 14.62 + 12.63 is 27.25