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A decimal is a numerical representation that includes a whole number part and a fractional part separated by a decimal point. The fractional part consists of digits representing less than one, such as tenths, hundredths, and thousandths.

Decimals are used to express quantities that are not whole numbers, showing precise measurements and quantities between whole number values.

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## Adding Decimals with Different Decimal Places

Like decimals have an equal number of digits after the decimal.

For Example, 0.15 and 2.25 are like decimals, whereas,

Unlike decimals, they have different numbers of digits after the decimal.

For Example, 7.31 and 5.825 are unlike decimals.

Here’s a step-by-step guide on how to add like decimals:

Step 1: Align the Decimal Points

Place the numbers vertically, aligning the decimal points.

4.37

+ 2.19

——-

Step 2: Add the Digits in the Ones Place

Start by adding the digits in the rightmost column (the ones place). 7 + 9 = 16. Write down 6 and carry over 1.

4.37

+ 2.19

——-

6

Step 3: Move Left and Add the Tenths Place

Move one column to the left (the tenths place) and add the digits in that column, including the carryover from the previous step. 1 (carryover) + 3 + 1 = 5.

4.37

+ 2.19

——-

56

Step 4: Move Left and Add the Hundredths Place

Move one more column to the left (the hundredths place) and add the digits. 4 + 2 = 7. Make sure to include the decimal point in the correct position based on the original numbers.

4.37

+ 2.19

——-

6.56

Step 1: Align the Decimal Points

Place the numbers you want to add vertically, aligning their decimal points. Convert unlike decimals to like decimals by adding the required number of zeros.

Example:

12.345

+  3.560

———

Start by adding the digits in the rightmost column (the ones place). Write down the sum below the line.

Example:

12.345

+  3.560

———

5

Step 3: Move to the Next Column

Move one column to the left (the tenths place) and add the digits in that column, including the carry from the previous step if there are any.

Example:

12.345

+  3.560

———

05

Repeat this process for each successive column, adding the digits and any carryover from the previous step and placing the decimal point accordingly.

Example:

12.345

+  3.560

———

15.905

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## Adding Decimals with Whole Numbers

To add a decimal with a whole number, convert the whole number into a decimal number. A whole number can be changed to a decimal by adding a decimal point after the whole number and writing the required number of zeros after the decimal point to make both addends of the same length.

Example: Add 3 + 4.93 + 5

Step 1: Convert whole numbers to decimals and make all decimals like decimals.

The highest decimal place is 2, so let’s rewrite all numbers as decimal numbers with 2 decimal places to make them like decimals.

3 = 3.00

4.93

5 = 5.00

Step 2: Now, place the numbers to add vertically, aligning their decimal points.

3.00

4.93

+5.00

———

12.93

## FAQs

#### What is the first step in adding decimals?

The first step is to align the decimal points of the numbers you want to add. It ensures that you’re adding digits that have the same place value.

#### How do I align decimals when adding?

To add decimals, align the numbers vertically by placing the decimal points directly above each other. If one number has fewer decimal places, add zeros to the end of that number to make the decimal places equal.

#### Can I add decimals and whole numbers together?

Yes, you can add decimals and whole numbers together. Treat the whole number as a decimal by adding a decimal point at the end of it, and then follow the same steps for adding decimals.

#### How do I write the final answer with the correct decimal point?

The final answer should have a decimal point placed in the same position as the original numbers. Make sure to count the same number of decimal places from the right as the original numbers.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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