Adding two decimal numbers
Set out the addition exactly as with whole numbers, with one extra rule: the decimal points must line up, one under the other. That way the tenths land under the tenths, the hundredths under the hundredths.
12.4 + 5.8 = 18.2 — the decimal points stay lined up at every step
- Line up the two numbers by the decimal point (if needed, add a 0 so both numbers have the same number of decimal places).
- Add column by column, starting from the right, carrying as usual.
- Put the decimal point back in the result, in exactly the same column as in the numbers you started with.
Subtracting two decimal numbers
Same idea: line up the decimal points, fill in with 0s if needed, then subtract column by column, carrying as in a normal column subtraction.
9.50 − 3.25 = 6.25
9.5 is written as 9.50 to have two decimal places, like 3.25
Multiplying a decimal by a whole number
Multiply as if the decimal point didn't exist (multiply the two whole numbers you get), then put the point back at the end, counting the number of decimal places in the starting number.
- Calculate 34 × 3 as if 3.4 were a whole number → 102.
- 3.4 had 1 decimal place → count 1 place in from the right of the result.
- 102 becomes 10.2.
3.4 × 3 = 10.2
Multiplying or dividing by 10, 100, 1,000
This is the quickest rule of all: just shift the decimal point, no working out needed.
- Multiplying by 10, 100, 1,000 → the point moves to the right (1, 2 or 3 places).
- Dividing by 10, 100, 1,000 → the point moves to the left (1, 2 or 3 places).
3.45 × 100 = 345 345 ÷ 100 = 3.45
Multiplying and dividing by 100 are two opposite movements of the point
Dividing a decimal by a whole number
Set out the division as a normal long division: bring the decimal point of the dividend straight down into the quotient the moment you reach it, then keep dividing as usual.
7.2 ÷ 4 = 1.8
72 ÷ 4 = 18, then the point goes back in the same spot as in 7.2
Estimating before calculating
As with whole numbers, it's useful to estimate the result before setting out the calculation, to check you haven't misplaced the decimal point. 7.8 + 4.3 should give "roughly 12" (8 + 4) — a result of 1.21 or 121 would immediately signal a mistake.
Mistakes to avoid
- Misaligning the decimal points in a column addition or subtraction — the most common mistake.
- Forgetting to put the decimal point back at the end of a multiplication.
- Moving the point the wrong way (left to divide, right to multiply).
- Forgetting that a 0 added after the decimal point doesn't change the number's value (5.8 = 5.80).
Worked exercises
4.25 + 3.6
6.3 × 100
8.4 ÷ 4
Now it's your turn!
On EasyMaths, your child practises calculating with decimal numbers with exercises that never repeat and instant marking.
Start the exercises →Frequently asked questions
How do you add two decimal numbers?
Like a normal column addition, lining up the decimal points carefully under each other (and so the tenths under the tenths, the hundredths under the hundredths). You add column by column starting from the right, exactly as with whole numbers.
How do you multiply a decimal number by 10, 100 or 1,000?
You move the decimal point to the right by as many places as there are zeros: 1 place for ×10, 2 places for ×100, 3 places for ×1,000. Example: 3.45 × 100 = 345.
How do you divide a decimal number by 10, 100 or 1,000?
You move the decimal point to the left by as many places as there are zeros: 1 place for ÷10, 2 places for ÷100. Example: 345 ÷ 100 = 3.45. It's the opposite movement to multiplying.