Adding & Subtracting Decimals

Q: Does adding zeros to the end of a decimal change its value?

No. $6.2$, $6.20$, and $6.200$ are all the same number. Zeros at the end of the decimal part only fill out columns so every place has a digit to work with.

Adding and subtracting decimals is regular column arithmetic with one extra rule: line up the decimal points, not the last digits. Once the points are stacked in a straight column, tenths sit over tenths and hundredths over hundredths, and the arithmetic works exactly like whole numbers.

The classic mistake is right-aligning the numbers like you would for $345 + 62$ . Do that with $3.75 + 1.4$ and you end up adding tenths to hundredths — digits that don't belong together. Stack the points first and that mistake becomes impossible.

Line up the decimal points

Write the numbers vertically so the decimal points form one straight column. Every place value then lines up automatically: ones over ones, tenths over tenths, hundredths over hundredths.

Add or subtract column by column from the right, carrying or regrouping as usual. The decimal point in the answer drops straight down from the column of points above it.

Fill the empty places with zeros

When one number has more decimal places than the other, pad the shorter one with zeros: $6.2$ becomes $6.20$ so it can meet $3.85$ place for place. The zeros change nothing about the value — $6.2$ and $6.20$ are the same number — but they give every column a digit and make regrouping painless.

This matters most in subtraction. Without the zero, students see the empty hundredths spot in $6.2 - 3.85$ and either skip the column or borrow incorrectly.

Whole numbers have a decimal point too

A whole number like $12$ can always be written as $12.00$ — the point sits just after the ones digit. So $12 - 4.35$ becomes $12.00 - 4.35$ , and now the usual routine takes over: points lined up, every column filled, subtract right to left.

Worked examples

Example 1: adding with different lengths

Add $3.75 + 1.4$ .

Line up the decimal points and pad with a zero

3.75 + 1.40

Add the hundredths, tenths, then ones

5.15

Answer: $5.15$

Example 2: subtracting with regrouping

Subtract $6.2 - 2.85$ .

Line up the points and write

6.2

6.20

6.20 - 2.85

Subtract column by column, regrouping as needed

3.35

Check:

3.35 + 2.85 = 6.20

✓

Answer: $3.35$

Example 3: subtracting from a whole number

Subtract $12 - 4.35$ .

Give

12

its decimal point and zeros

12.00 - 4.35

Subtract column by column

7.65

Answer: $7.65$

Try one yourself

Common questions

Why do I line up the decimal points instead of the last digits?

Because you can only add digits that share a place value — tenths with tenths, hundredths with hundredths. Lining up the points stacks matching places automatically. Right-aligning the digits mixes places and gives a wrong answer.

Does adding zeros to the end of a decimal change its value?

No. $6.2$ , $6.20$ , and $6.200$ are all the same number. Zeros at the end of the decimal part only fill out columns so every place has a digit to work with.

Where does the decimal point go in my answer?

Straight down from the column of decimal points above it. If the points in the problem are stacked, the point in the answer is already placed for you.

How do I subtract a decimal from a whole number?

Write the whole number with a decimal point and zeros — $12$ becomes $12.00$ — then line up the points and subtract normally.

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