Why do I have to fill in zeros after the decimal point?

Filling in zeros helps you see the columns clearly and makes sure you don't skip a place-value position. When you write 10.30 instead of 10.3, the hundredths column is obvious, and you're less likely to make an error. The zeros don't change the value (10.30 = 10.3), but they protect you from careless mistakes by making the place-value structure visible.

What if the two numbers have a different number of decimal places?

Always rewrite both numbers so they have the same number of decimal places by adding zeros to the right. If you're adding 7.2 + 3.456, rewrite 7.2 as 7.200 so both have three decimal places. Then align and add normally. This keeps your columns straight and prevents errors.

Does the order matter in addition? What about subtraction?

In addition, order does not matter: 5.3 + 2.1 = 7.4 and 2.1 + 5.3 = 7.4. In subtraction, order absolutely matters: 5.3 − 2.1 = 3.2, but 2.1 − 5.3 = −3.2. Always put the larger number on top if you want a positive answer, or be clear about which number you're subtracting from which.

How do I know if my answer is reasonable?

Round each number to the nearest whole number and do the calculation mentally. For 8.2 + 4.7, round to 8 + 5 = 13, and your exact answer (12.9) should be close to 13. If your answer is way off (like 1.29 or 129), you've likely made an error with the decimal point placement.

M6MATH-4.2

Adding & Subtracting Decimals

Learn how to add and subtract decimals by lining up place values and using the standard algorithm—essential skills for money, measurement, and real-world math.

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A voice-first session with the Crimsora tutor on Adding & Subtracting Decimals, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

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What this lesson covers

Adding and subtracting decimals looks like adding and subtracting whole numbers, but there's one critical step that makes the difference between a correct answer and a big mistake: lining up the decimal points. In this lesson, you'll learn to use the standard algorithm to add and subtract multi-digit decimals fluently. This skill matters everywhere—when you calculate the total cost of items, work with measurements in science, or track changes in data. We'll focus on why alignment works and how to avoid common errors that trip up students.

Why Alignment Matters: Place Value

When you add or subtract whole numbers, you line up the ones place, tens place, and hundreds place. Decimals extend this system to the right of the decimal point: tenths, hundredths, thousandths. Each digit belongs in its own place-value column, and only digits in the same column can be combined.

When you write 3.4 + 2.15, it might look tempting to just write the digits in order and add: 3415. But that's wrong because 3.4 means 3 ones and 4 tenths, while 2.15 means 2 ones and 1 tenth and 5 hundredths. To add these correctly, you must line them up so that tenths are under tenths and hundredths are under hundredths:

\begin{array}{r} 3.40 \\ + 2.15 \\ \hline 5.55 \end{array}

Notice that we rewrote 3.4 as 3.40. This doesn't change the value—it just fills in the empty hundredths place. Many students skip this step and get confused; writing the zeros in makes the columns line up clearly.

The Standard Algorithm: Step by Step

The standard algorithm for adding and subtracting decimals is almost identical to what you do with whole numbers. Here are the steps:

Step 1: Align the decimal points vertically. Write one number above the other so the decimal points are in the same column.

Step 2: Fill in zeros if needed. Write zeros in empty decimal places so both numbers have the same number of digits after the decimal point. This prevents confusion and errors.

Step 3: Add or subtract from right to left, starting with the smallest place value (the rightmost digit). Carry or borrow as usual.

Step 4: Place the decimal point in your answer directly below the decimal points in the problem.

For example, subtract 5.23 from 8.7:

\begin{array}{r} 8.70 \\ - 5.23 \\ \hline 3.47 \end{array}

Start on the right: 0 − 3 requires borrowing. Borrow 1 from the 7 tenths, making it 6 tenths, and the 0 hundredths becomes 10 hundredths. Now 10 − 3 = 7. Then 6 − 2 = 4. Finally, 8 − 5 = 3. The decimal point stays in its place in the answer.

Common Errors and How to Avoid Them

The most common mistake is forgetting to align decimal points. Students sometimes line up the ones digits instead and end up adding 8.7 − 5.23 as if they were doing 87 − 523 in disguise. Always check that the decimal points form a vertical line before you start.

A second frequent error is not filling in zeros. When one number has more decimal places than another, students may skip them and lose track of place value. Writing 8.70 instead of just 8.7 takes one extra second and prevents errors.

Third, some students forget to include the decimal point in the answer or put it in the wrong place. After you add or subtract, the decimal point should line up exactly with the decimal points above it. A quick check: if you're adding 2.5 + 3.2, the answer should be close to 2 + 3 = 5, so 5.7 makes sense. If you wrote 57 or 0.57, you've made an error.

Finally, careless arithmetic in the standard steps. Adding and subtracting decimals uses the same carrying and borrowing rules as whole numbers. If you're unsure whether you borrowed correctly, go through it again slowly or check your work by adding the answer back to the number you subtracted.

Checking Your Work

A good habit is to estimate before you compute. Round each decimal to the nearest whole number and add or subtract mentally. For 4.82 + 2.13, round to 5 + 2 = 7. Then compute exactly and get 6.95, which is close to 7, so it passes the sense check.

You can also verify by adding or subtracting in the opposite direction. If you computed 8.7 − 5.23 = 3.47, check by computing 3.47 + 5.23 and see if you get 8.7. If the numbers work out, you're correct.

These checks take only a few seconds and help you catch errors before you move on. Building this habit now makes you more confident and accurate in all math work ahead.

Key terms

Decimal point.: The dot that separates the whole-number part from the fractional part. In 5.23, the decimal point separates 5 ones from 2 tenths and 3 hundredths.
Place value.: The value a digit holds based on its position. In 5.23, the 2 is in the tenths place (worth 0.2), and the 3 is in the hundredths place (worth 0.03).
Tenths place.: The first digit to the right of the decimal point, representing one out of ten equal parts. In 0.6, the 6 is in the tenths place.
Hundredths place.: The second digit to the right of the decimal point, representing one out of one hundred equal parts. In 0.43, the 3 is in the hundredths place.
Align.: To arrange numbers so that decimal points and place-value columns line up vertically, allowing correct addition or subtraction.
Regroup (carry or borrow).: To move 10 units from one place value to another when adding (carry) or subtracting (borrow) causes a digit to be too large or too small.
Standard algorithm.: The step-by-step method taught in school for adding, subtracting, multiplying, or dividing. For decimals, it involves aligning decimal points and working right to left.

Worked example

Calculate 12.6 + 8.47 using the standard algorithm.

Step 1: Write the numbers vertically and align the decimal points.

\begin{array}{r} 12.6 \\ + 8.47 \\ \hline \end{array}

Step 2: Fill in any missing zeros. The top number has only one decimal place; the bottom has two. Rewrite 12.6 as 12.60 so both have two decimal places.

\begin{array}{r} 12.60 \\ + 8.47 \\ \hline \end{array}

Step 3: Add from right to left, starting with the hundredths place. In the hundredths column, 0 + 7 = 7. In the tenths column, 6 + 4 = 10. Write the 0 and carry the 1 to the ones place. In the ones column, 1 (carried) + 2 + 8 = 11. Write the 1 and carry the 1 to the tens place. In the tens place, 1 (carried) + 1 = 2.

\begin{array}{r} {}^1 12.60 \\ + 8.47 \\ \hline 21.07 \end{array}

Step 4: Place the decimal point in the answer directly below the decimal points above. The answer is 21.07.

Check: 12.6 is about 13 and 8.47 is about 8, so 13 + 8 = 21, and 21.07 is close to 21. ✓

Practice questions

Add: 7.34 + 5.82

Answer: 13.16

Align the decimal points vertically. Both numbers already have two decimal places, so no zeros need to be added. Add from right to left: 4 + 2 = 6, then 3 + 8 = 11 (write 1, carry 1), then 1 (carried) + 7 + 5 = 13. The decimal point goes in the same column as the ones above. Many students forget to carry the 1 from the tenths place to the ones place, giving a wrong answer of 12.16.

Subtract: 10.3 − 4.56

Answer: 5.74

Align the decimal points and rewrite 10.3 as 10.30 to match two decimal places. Starting from the right: 0 − 6 requires borrowing. Borrow 1 from the 3 tenths, making it 2 tenths and 0 hundredths becomes 10 hundredths. Now 10 − 6 = 4. Next, 2 − 5 in the tenths column requires borrowing again. Borrow 1 from the 0 ones... wait, there's no ones place to borrow from directly. Borrow 1 from the tens place (10 becomes 0), making the ones place 10. Now borrow 1 from the ones (making it 9), so the tenths place becomes 12. Then 12 − 5 = 7. Finally, 9 − 4 = 5. The answer is 5.74. This problem is tricky because it requires borrowing twice; students often stop after the first borrow or skip a step, leading to 5.24 or other incorrect answers.

Maria buys a notebook for 3.45 dollars and a pen for 1.28 dollars. What is the total cost?

Answer: 4.73 dollars

Set up the addition: 3.45 + 1.28. Align the decimal points (both have two places, so no zeros needed). Add from right to left: 5 + 8 = 13 (write 3, carry 1), then 1 (carried) + 4 + 2 = 7, then 3 + 1 = 4. The total is 4.73 dollars. A common error is misplacing the decimal (writing 47.3 or 0.473), which doesn't make sense in context: 47.3 dollars is way too expensive for these items, and 0.473 dollars is far too cheap.

FAQ

Why do I have to fill in zeros after the decimal point?: Filling in zeros helps you see the columns clearly and makes sure you don't skip a place-value position. When you write 10.30 instead of 10.3, the hundredths column is obvious, and you're less likely to make an error. The zeros don't change the value (10.30 = 10.3), but they protect you from careless mistakes by making the place-value structure visible.
What if the two numbers have a different number of decimal places?: Always rewrite both numbers so they have the same number of decimal places by adding zeros to the right. If you're adding 7.2 + 3.456, rewrite 7.2 as 7.200 so both have three decimal places. Then align and add normally. This keeps your columns straight and prevents errors.
Does the order matter in addition? What about subtraction?: In addition, order does not matter: 5.3 + 2.1 = 7.4 and 2.1 + 5.3 = 7.4. In subtraction, order absolutely matters: 5.3 − 2.1 = 3.2, but 2.1 − 5.3 = −3.2. Always put the larger number on top if you want a positive answer, or be clear about which number you're subtracting from which.
How do I know if my answer is reasonable?: Round each number to the nearest whole number and do the calculation mentally. For 8.2 + 4.7, round to 8 + 5 = 13, and your exact answer (12.9) should be close to 13. If your answer is way off (like 1.29 or 129), you've likely made an error with the decimal point placement.

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