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.

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.

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 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: 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 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

Tips and Tricks for Adding Decimals

• We always start adding decimals from the right-hand side, like in the case of the addition of two whole numbers.
• The decimal points are always aligned below the decimal point.
• The addition of two decimal numbers can be treated as the addition of two whole numbers initially and the decimal places can be placed in the end to avoid confusion.

☛Related Articles

• Decimals and Fractions
• Addition and Subtraction of Decimals
• Multiplying Decimals
• Comparing Decimals

What is the Rule for Adding Decimals?

For adding decimals, we need to remember the following rules that would make the process of addition easier.

• Align the decimal numbers in such a manner that they are placed in the correct column according to their place values.
• Remember to convert the decimal numbers to like decimals, wherever needed.
• Add zeros in the places wherever the length of the decimal numbers is not equal.
• Finally, add the numbers and place the decimal point aligned with the given decimal points.

How to Add Decimals By Regrouping?

While adding decimals, the regrouping of numbers is done in the same way as in the addition of whole numbers. The important thing to be kept in mind is that the decimal point and all the numbers should be aligned correctly according to the place values. Regrouping in decimals is done if the sum of the addends is greater than 9 in any of the columns. Then, the extra digit is carried over to the preceding column. For example, if we need to add 3.6 and 2.9, we will start adding the tenths column, which is 6 + 9 = 15. But we cannot place 15 here since only one digit is placed under one column. So, we will write 5 in this column and carry over 1 to the ones column. This is how we regrouped 15. Then, moving on to the ones column, we will add the given numbers along with this carry-over. This will be, 3 + 2 + 1 (carry-over) = 6.5. Therefore, the sum will be 6.5

How to Add Decimals with Whole Numbers?

We add decimals with whole numbers in a very simple way. We place a decimal point after the whole number and write the required number of zeros after the decimal so as to make both the numbers of the same length. In other words, we change them to like decimals and then add them. For example, if we need to add 5 + 3.23, we will change 5 to 5.00 and then add it to 3.23. So, 5.00 + 3.23 = 8.23

How to Add Decimals and Fractions?

In order to add decimals and fractions, we can use the following steps. Let us understand this by adding 14.32 + 1/4. Here 14.32 is a decimal and 1/4 is a fraction.

• Step 1: Convert the fraction into its decimal form. So, the fraction 1/4 is written as 0.25 in the decimal form.
• Step 2: Write the numbers such that the decimals are aligned according to their place values.Here, 14.32 + 0.25
• Step 3: Place zero in the places if the length of decimal numbers is not the same and add the numbers as we add whole numbers, starting from the right and move to the left. Here they are of the same length, therefore, we can move on.
• Step 4: So, the sum of the given numbers is 14.32 + 0.25 = 14.57

How to Add Decimals with Different Decimal Places?

If the given set of decimal numbers have different number of digits after the decimal point, they are called unlike decimal fractions. In this case, we count the number of digits after the decimal point in both the numbers and identify the higher one in them. After this step, we add the required number of zeros to the smaller decimal number so that it becomes of the same length as the other number. After this, we add the decimals numbers. For example, if we need to add 23.3 and 12.456, we will make it 23.300 + 12.456 and then add them. So, the sum will be 23.300 + 12.456 = 35.756

What are the Steps for Adding Decimals?

There are some basic steps that are used for adding decimals.

• Step 1: First of all, align the decimal numbers according to their place values.
• Step 2: Then, convert the decimal numbers to like decimals, if needed.
• Step 3: Finally, add the numbers and place the decimal point aligned with the given decimal points.

How is Adding Decimals Similar to Subtracting Decimals?

Adding decimals is similar to subtracting decimals because some common rules are followed in both the operations.

• In the addition and subtraction of decimals, we need to place the decimal numbers one below the other in such a way that they are aligned according to their place values along with the decimal point.
• We also need to change the given decimal fractions to like decimals so that the process of addition or subtraction becomes easier.
• After converting the given decimals to like decimals, by adding the required number of zeros, we add or subtract the given numbers in the regular way in which we add or subtract whole numbers.