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Decimals

Decimal Calculator

Add, subtract, multiply and divide decimals with the working shown at every step. Learn the key rules: aligning decimal points for addition and subtraction, counting decimal places for multiplication, and converting decimals when dividing.

Decimal calculator

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Enter any decimal numbers — positive or negative.

Step by step calculations

Decimal Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Decimals in everyday life

Shopping: £3.47 + £8.99 at the till. Petrol: 153.9p per litre × 42 litres. Splitting a restaurant bill: £47.25 ÷ 3 people = £15.75 each. Every money calculation you've done since childhood uses decimal arithmetic. The rules are simple — but easy to slip on when decimal points shift.

Worked example

"Add £12.45 + £3.70. Then find 1.4 × 2.5."

Addition: align decimal points

12.45

+ 3.70

= 16.15

─────────

Multiply: 14 × 25 = 350

Decimal places: 1 + 1 = 2

Result: 3.50

For addition/subtraction: align decimal points. For multiplication: count decimal places in both numbers, then place the point.

Common mistake to avoid

  • ✗ Aligning decimal points when multiplying: for multiplication you don't align points — you ignore them until the end, then count total decimal places. Only addition and subtraction require alignment.
Good to know

Key rules for decimal arithmetic

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Adding & subtracting — align the point
The golden rule: always line up the decimal points before adding or subtracting. Pad shorter decimals with zeros on the right so both numbers have the same number of decimal places. Then add or subtract column by column, exactly as you would with whole numbers — the decimal point in the answer is directly below the others.
12.45
+ 3.70
──────
16.15
×
Multiplying — count the decimal places
Ignore the decimal points and multiply the numbers as if they were whole integers. Count the total number of decimal places in both numbers combined. In the answer, count that many places from the right and insert the decimal point. You never need to align decimal points when multiplying — only count them.
2.5 × 1.4
→ 25 × 14 = 350
→ 1 dp + 1 dp = 2 dp
→ 350 becomes 3.50 = 3.5
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Dividing — clear the decimal first
If the divisor (the number you're dividing by) has decimal places, multiply both numbers by a power of 10 to make it a whole number. For example, if dividing by 0.3 (1 decimal place), multiply both by 10. The result is unchanged because you're scaling both sides equally — it just makes the division easier.
8.4 ÷ 0.3
→ ×10 both sides
→ 84 ÷ 3 = 28

7.5 ÷ 0.25 → ×100 → 750 ÷ 25 = 30
0.3̄
Recurring decimals
Some divisions produce a decimal that repeats forever. For example, 1 ÷ 3 = 0.333… and 1 ÷ 7 = 0.142857142857… These are called recurring (or repeating) decimals and are written with a dot above the repeating digit: 0.3̄. Every fraction produces either a terminating or a recurring decimal — never a random one.
1 ÷ 3 = 0.333333… = 0.3̄
1 ÷ 6 = 0.166666… = 0.1̄6̄
1 ÷ 7 = 0.142857142857…

Fractions with denominator 2 or 5
only → always terminate.