Adding and Subtracting Decimals

Decimals are place value in action

Money, measurements and sports times all use decimals. A decimal is just another way to write numbers smaller than one, using place value. The digits after the decimal point stand for tenths, hundredths and thousandths. So in 3.45, the 3 is 3 ones, the 4 is 4 tenths, and the 5 is 5 hundredths. If you would like a fuller introduction, see our Decimals Explained lesson.

Adding and subtracting decimals works exactly like adding and subtracting whole numbers — with one golden rule: line up the decimal points.

The golden rule: line up the points

Rule: Write the numbers one above the other so the decimal points line up. This keeps ones under ones, tenths under tenths, and hundredths under hundredths.

When you line up the points, the place values automatically match. You then add or subtract column by column, right to left, just as you always have. Finally, bring the decimal point straight down into the answer.

A helpful tip: if one number has fewer decimal places, fill the gap with a zero. For example, write 3.4 as 3.40 so it matches 2.15. This does not change the value, because 3.4 and 3.40 are the same amount.

Adding decimals

Example 1 — Work out 3.4 + 2.15.

1. Line up the decimal points and add a trailing zero so both have two decimal places:

     3.40
   + 2.15

1. Add the hundredths: 0 + 5 = 5.
2. Add the tenths: 4 + 1 = 5.
3. Bring down the decimal point, then add the ones: 3 + 2 = 5.
4. So 3.4 + 2.15 = 5.55.

Example 2 — Work out 0.6 + 0.7 (with carrying).

1. Line up the points:

     0.6
   + 0.7

1. Add the tenths: 6 + 7 = 13 tenths. That is 1 whole and 3 tenths, so write 3 in the tenths column and carry 1 to the ones.
2. Add the ones: 0 + 0 + 1 (carried) = 1.
3. So 0.6 + 0.7 = 1.3.

Subtracting decimals

Subtraction follows the same line-up rule, and you borrow across columns just like with whole numbers.

Example 3 — Work out 7.8 − 3.45.

1. Line up the points and write 7.8 as 7.80:

     7.80
   − 3.45

1. Hundredths: you cannot take 5 from 0, so borrow from the tenths. The 8 tenths becomes 7, and the 0 becomes 10: 10 − 5 = 5.
2. Tenths: 7 − 4 = 3.
3. Bring down the point, then ones: 7 − 3 = 4.
4. So 7.8 − 3.45 = 4.35.

Example 4 — Work out 5.0 − 2.4.

1. Line up the points:

     5.0
   − 2.4

1. Tenths: you cannot take 4 from 0, so borrow. The 5 ones becomes 4, and the 0 tenths becomes 10: 10 − 4 = 6.
2. Ones: 4 − 2 = 2.
3. So 5.0 − 2.4 = 2.6.

A reference table

Problem	Lined up (with zeros)	Answer
1.2 + 3.45	1.20 + 3.45	4.65
0.9 + 0.8	0.9 + 0.8	1.7
6.5 − 2.3	6.5 − 2.3	4.2
8.0 − 3.6	8.0 − 3.6	4.4
4.75 + 1.5	4.75 + 1.50	6.25

Why lining up the points matters

It is tempting to ignore the decimal point and just push the numbers to the right, but that gives wrong answers. Here is the why: you can only add digits that mean the same thing. Tenths can be added to tenths, and hundredths to hundredths, but a tenth is ten times bigger than a hundredth, so they cannot be combined directly.

Lining up the decimal points guarantees that every column contains digits of the same place value. Think about money: £3.40 means 3 pounds and 40 pence, while £2.15 means 2 pounds and 15 pence. You add pounds to pounds and pence to pence — you would never add the 4 (tens of pence) to the 1 (also tens of pence) unless they were in the same column. The decimal point is the marker that keeps every place value in its proper place.

A practice activity

Use real or pretend money — coins and notes work perfectly.

1. Lay out £3.40 (three £1 coins, four 10p coins) and £2.15 (two £1 coins, one 10p, one 5p).
2. Combine them. Count the pounds: 3 + 2 = £5. Count the pence: 40p + 15p = 55p.
3. Together that is £5.55 — exactly what the column method gives for 3.40 + 2.15.
4. Now practise subtracting: start with £5.00 and "spend" £2.40. How much is left? Borrowing in pence gives £2.60.

Then try these on paper (answers below): (a) 2.5 + 1.36, (b) 0.7 + 0.5, (c) 9.4 − 3.2, (d) 6.0 − 2.85.

Answers: (a) 3.86, (b) 1.2, (c) 6.2, (d) 3.15.

Where this leads

Adding and subtracting decimals is the foundation for working with money, measurement and later for multiplying and dividing decimals. It connects closely to fractions, since a decimal is just a fraction with a denominator of 10, 100 or 1000. To see those links, explore Decimals Explained. The one habit to keep forever: line up the decimal points first.