Number & Operations in Base Ten

Adding & Subtracting Decimals

Adding and subtracting decimals to the hundredths place.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Reading & Comparing Decimals

Why Lining Up the Decimal Point Matters

What do you think would go wrong if you added 3.4 and 2.15 by just lining up the rightmost digits, the way you might for whole numbers? Try it both ways — lined up on the right, and lined up by the decimal point — and compare the two results.

Lining up on the right adds a tenths digit to a hundredths digit, mixing two different place values together — the same mistake as adding 3 tens to 2 ones and calling it 5. Lining up the decimal points instead makes sure tenths add with tenths and hundredths add with hundredths, exactly the way whole-number addition always lines up matching place values.

Worked Example — Adding Decimals with Different Lengths

Add 3.4 + 2.15. Line up the decimal points, writing 3.4 as 3.40 so both numbers show hundredths. Add each place value: hundredths 0 + 5 = 5, tenths 4 + 1 = 5, ones 3 + 2 = 5. The sum is 5.55.

Worked Example — Subtracting Decimals with Borrowing

Subtract 6.2 − 3.45. Line up the decimal points, writing 6.2 as 6.20. Subtracting the hundredths, 0 − 5, requires borrowing: borrow a tenth, making it 10 − 5 = 5, and reducing the tenths digit. Working through the borrowing carefully gives 2.75.

Tip

Writing a trailing zero onto the shorter decimal before adding or subtracting — the same technique from the last lesson's comparisons — makes lining up the columns much less error-prone.

Common Mistakes

Lining up decimal numbers by their rightmost digit instead of by their decimal point, especially when the numbers have a different count of decimal digits.
Always align the decimal points first — this automatically lines up tenths with tenths and hundredths with hundredths, no matter how many digits each number has.
Forgetting to carry the decimal point straight down into the answer.
The decimal point in the answer belongs in the exact same column as the decimal points in the two numbers being added or subtracted — write it in first as a placeholder before filling in the digits.

Key Takeaways

Adding and subtracting decimals requires lining up the decimal points so matching place values combine correctly.
Writing trailing zeros makes two decimals of different lengths easier to line up.
The decimal point in the answer lines up directly with the decimal points in the original numbers.

Summary

Lining up decimal points keeps addition and subtraction accurate by combining only matching place values. The final lesson in this unit extends decimal arithmetic to multiplication and division.

Track your progress

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