Decimal Addition
Adding decimals follows exactly the same column method as adding whole numbers. The only extra rule is that decimal points must be aligned. Once the points line up, you add as normal.
The Golden Rule – Align the Decimal Point
Every decimal number has a decimal point. In column addition, every decimal point must sit in the same vertical position. This automatically aligns the tenths under tenths, hundredths under hundredths, and so on.
3.4 + 12.57 → write as 03.40 + 12.57, align points, then add
Padding with Zeros
If one number has fewer decimal places than another, add trailing zeros to fill the gap. This does not change the value but keeps the columns tidy.
| Original | Padded for alignment |
|---|---|
| 5.3 + 2.47 | 5.30 + 2.47 |
| 0.6 + 4.125 | 0.600 + 4.125 |
Worked Examples
Example 1 – Tenths
3 . 2 + 5 . 6 ------- 8 . 8
Tenths: 2+6=8. Ones: 3+5=8. Answer: 8.8
Example 2 – Hundredths with Carrying
¹ 4 . 7 8 + 3 . 6 5 --------- 8 . 4 3
Hundredths: 8+5=13 → 3 carry 1. Tenths: 7+6+1=14 → 4 carry 1. Ones: 4+3+1=8. Answer: 8.43
Example 3 – Different Decimal Places
Calculate 6.4 + 2.135
6 . 4 0 0 + 2 . 1 3 5 ----------- 8 . 5 3 5
Answer: 8.535
Real-Life Applications
- Money: £4.75 + £2.38 = £7.13
- Measurements: 1.45 m + 0.85 m = 2.30 m
- Science: Adding measurements to two or three decimal places.
Key Takeaways
- Always align decimal points before adding.
- Pad with trailing zeros where needed.
- Carry works exactly as it does with whole numbers.
- The decimal point in the answer sits directly below those in the calculation.
Practice Questions
- Calculate 3.4 + 5.2.
- Calculate 7.85 + 4.36.
- Add 12.5 + 3.75.
- A piece of wood is 1.35 m long. Another is 0.8 m. What is the total length?
- Calculate 0.456 + 1.78 + 3.2.