Adding and Subtracting Decimals

You are at the shop. A comic costs £3.75 and a bag of sweets costs £2.40. Have you got enough coins for both? To find out you have to add two decimals together:

3.75 + 2.40 = \;?

Adding and subtracting decimals is one of the most useful skills you will ever learn — you use it to add up prices, to work out your change, to measure and cut lengths, to keep score. And it works exactly like ordinary column addition, with one golden rule that makes everything fall into place:

Why does that matter so much? Because the point is the fence that keeps every digit in its proper column: ones under ones, tenths under tenths, hundredths under hundredths. Stack the points and every digit lands where it belongs — then you just add or subtract column by column, exactly like whole numbers.

The method, step by step

Here is the whole recipe. Follow it every single time and you will never go wrong.

  1. Stack the numbers with their decimal points lined up vertically.
  2. Pad with zeros so every number has the same number of decimal places — a gap on the right is worth nothing, so filling it with 0 never changes the value (2.4 = 2.40 = 2.400).
  3. Add or subtract column by column, starting from the right, carrying or borrowing exactly as with whole numbers.
  4. Bring the decimal point straight down into the answer, right below the ones above it.

Worked example 1 — the shopping total

Back to the comic and the sweets: 3.75 + 2.40. Both prices already have two decimal places (the 2.40 was padded from 2.4), so the columns match. Stack and add: 

   3.75
 + 2.40
 ------
   6.15
   1        (carried ten from the tenths column)

Hundredths: 5 + 0 = 5. Tenths: 7 + 4 = 11 — write 1, carry 1. Ones: 3 + 2 + 1 = 6. The point drops straight down, so the two things cost £6.15 altogether.

Worked example 2 — subtracting from a whole number

You have a 10 cm strip of paper and you snip off 3.6 cm. How much is left? That is 10 - 3.6. A whole number hides a decimal point on its right, so write 10 as 10.0 to match the one decimal place: 

   10.0
 -  3.6
 ------
    6.4

Tenths: you can't do 0 - 6, so borrow one whole (ten tenths) from the ones column — 10 - 6 = 4. Ones: 9 - 3 = 6. So 10 - 3.6 = 6.4 cm left.

Worked example 3 — three prices at once

The rule doesn't mind how many numbers you stack. Add 1.5, 0.75 and 2.05 — pad 1.5 to 1.50 so all three have two decimal places, then add straight down: 

   1.50
   0.75
 + 2.05
 ------
   4.30

Hundredths: 0 + 5 + 5 = 10 — write 0, carry 1. Tenths: 5 + 7 + 0 + 1 = 13 — write 3, carry 1. Ones: 1 + 0 + 2 + 1 = 4. The total is 4.30, which we can tidy to 4.3.

This is the single most common decimal mistake in the world — and it costs people real money. When you add 3.75 + 2.4, it is tempting to shove the numbers hard to the right so their last digits line up, like this wrong stacking: 

   3.75      ✗ WRONG — last digits lined up
 + 2.4

Now the 4 is sitting under the 5 — hundredths under hundredths — but the 4 means four tenths! You would be adding four tenths to five hundredths, which is nonsense, and you'd get a wildly wrong answer.

The fix is the golden rule. Pad 2.4 to 2.40 and line up the points, so the 4 sits under the 7 — both tenths, where it belongs: 

   3.75      ✓ RIGHT — points lined up
 + 2.40
 ------
   6.15

Always trust the point, never the ragged right-hand edge.

Look closely at a supermarket receipt, a bank statement, or a spreadsheet of prices. Every amount is printed with its decimal point in a perfectly straight vertical line down the page: 

    3.75
    2.40
   12.09
    0.99

That isn't just tidiness or good looks. It is the golden rule in action! By lining the points up, the machine (or the shopkeeper) can add the whole column straight down and get the right answer every time. The same place-value idea — ones under ones, tens under tens — is exactly what makes our entire number system work. Line up the columns, and arithmetic almost does itself.

See it explained