Addition of Decimals

Understanding how to add decimals is an important skill in math. Like adding whole numbers, the process involves lining up the numbers and adding them column by column. However, the key to adding decimals correctly is to make sure the decimal points line up.

Decimal places and values

Before we talk about addition, let's remember what decimals are. Decimals are numbers that have a whole part and a fractional part, separated by a decimal point. For example, in the number 3.75, 3 is the whole part, and 75 is the fractional part.

Decimals are based on powers of ten. The number 3.75 is read as "three and seventy-five hundredths" because 7 is in the tenths place (one-tenth or 0.1) and 5 is in the hundredths place (one-hundredth or 0.01).

Lining up decimals for addition

When you add decimals, it's necessary to line up the decimal points vertically, just like the digits are lined up in whole-number addition. For example, if we want to add 12.3 and 3.45, we write them like this:

  12.30
+ 3.45

Note that we added an extra zero to 12.3 to make it 12.30. This does not change the value of the number, it is just a placeholder to help align the decimal places.

Adding columns

After you have lined up the numbers, start adding from the rightmost column, moving left, just like with whole numbers.

In our example:

  12.30
+ 3.45

Starting from the hundredths place:

• Add 0 and 5, which equals 5.

In tenth place:

• Add 3 and 4, which equals 7.

Place the decimal point directly below the other decimal points in your total.

Visit unit location:

• Add 2 and 3, which equals 5.

Finally, in the tens place:

• Add 1 and 0 (there is no number to add 1 to the tens place of the second number), which equals 1.

So the complete sum looks like this:

  12.30
+ 3.45
  15.75

The answer is 15.75.

More examples

Example 1: Adding two decimals with different decimal places

Let's look at another example where we add 7.6 and 25.123.

  7.600
+25.123

Again, line up the decimal points vertically.

Add hundredths:

• 0 + 3 = 3

Add tenths:

• 0 + 2 = 2

Add hundredths:

• 6 + 1 = 7

Add the decimal point:

Visit the unit location:

• 7 + 5 = 12 (write 2 and carry 1)

Go to the tens place:

• carry 1 + 2 = 3

The calculation is as follows:

  7.600
+25.123
 32.723

The result is 32.723.

Example 2: Adding more than two decimals

Now, let's try adding three numbers: 8.32, 4.067, and 12.1.

  8.320
+ 4.067
+12.100

Vertically aligned with decimals:

Start with the thousandths:

• 0 + 7 + 0 = 7

Add hundredths:

• 2 + 6 + 0 = 8

Add tenths:

• 3 + 0 + 1 = 4

Add the decimal point:

Visit the unit location:

• 8 + 4 + 2 = 14 (write 4 and carry forward 1)

Move to tens:

• carry 1 + 1 = 2

The calculation should be as follows:

  8.320
+ 4.067
+12.100
 24.487

The result is 24.487.

Practice problems

Sometimes the best way to learn is to practice. Solve these problems by lining up the decimals and adding them column by column.

1. 5.67 + 2.3 = ?
2. 9.456 + 3.245 + 0.5 = ?
3. 13.05 + 2.789 = ?

Key tips to remember

• Always line up the decimal points before adding.
• Make sure each number has the same number of digits to the right of the decimal point, adding zeros as placeholders if necessary.
• After adding each column, be sure to place the decimal point in the answer just below the other decimal points.
• If a column totals 10 or more, carry it forward as you would with whole numbers.

Conclusion

Adding decimals is very similar to adding whole numbers. By making sure the decimal points are aligned, you maintain the correct place value, which leads to an accurate sum. If each number has a different number of decimal places, remember to adjust it with additional zeros. With practice, adding decimals becomes a smooth and straightforward process.

To master adding decimals, practice regularly and verify your work by estimating the answer beforehand. This can help you determine if your final answer is reasonable and correct.

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