Adding Decimals — Definition, Formula & Examples
Adding decimals is the process of finding the sum of two or more numbers that have a decimal point. The key rule is to line up the decimal points vertically before you add.
Decimal addition is performed by aligning the addends so that their decimal points occupy the same column, padding with trailing zeros where necessary to equalize the number of decimal places, and then summing column by column from right to left, carrying as needed.
How It Works
Write the numbers in a column so the decimal points are directly above each other. If one number has fewer decimal places, add zeros to the right so both numbers have the same length. Then add each column from right to left, just like you would with whole numbers. Place the decimal point in the answer directly below the other decimal points.
Worked Example
Problem: What is 12.6 + 3.45?
Line up the decimal points: Write 12.6 above 3.45, making sure the decimal points are aligned. Add a zero to 12.6 so both numbers have two decimal places.
Add from right to left: Hundredths: 0 + 5 = 5. Tenths: 6 + 4 = 10, write 0 and carry 1. Ones: 2 + 3 + 1 = 6. Tens: 1.
Answer: 16.05
Why It Matters
Adding decimals shows up every time you handle money — for example, totaling prices at a store or calculating change. It also builds the foundation for working with measurements in science and for adding fractions once you convert them to decimal form.
Common Mistakes
Mistake: Not lining up the decimal points and instead pushing all digits to the right, treating 12.6 + 3.45 like 126 + 345.
Correction: Always stack the numbers so the decimal points are in the same column. Use trailing zeros (12.60) to keep the columns aligned.