Adding Decimals – Align and Add
Adding decimals uses exactly the same method as adding whole numbers. The key step is aligning the decimal points so that digits of the same place value are always in the same column.
Misaligning decimal points is one of the most common arithmetic errors people make outside school, because unlike whole-number addition, decimal addends are rarely the same length — a receipt might list £4.5, £12.99, and £0.75 all in one column. Padding the shorter numbers with trailing zeros (4.50, 12.99, 0.75) before adding removes the ambiguity entirely and is exactly what a checkout till or spreadsheet does internally before summing a column of prices.
The Golden Rule
Always line up the decimal points. Pad shorter numbers with trailing zeros if needed. Then add column by column, right to left, carrying just as you would with whole numbers. The decimal point in the answer goes directly below the decimal points in the question.
Try It: 12.4 + 3.75
Pad the shorter decimal with a zero, add column by column with carrying, then drop the decimal point straight down.
Simple Addition
Ones: 3+2=5. Tenths: 4+5=9. Answer: 5.9.
Write 1.8 as 1.80. Hundredths: 7+0=7. Tenths: 6+8=14, write 4 carry 1. Ones: 4+1+1=6. Answer: 6.47.
Addition Requiring Carrying
Hundredths: 5+8=13, write 3 carry 1. Tenths: 9+6+1=16, write 6 carry 1. Ones: 7+3+1=11, write 1 carry 1. Tens: 0+0+1=1. Answer: 11.63.
Pad 2.64 as 2.640. Thousandths: 5+0=5. Hundredths: 7+4=11, write 1 carry 1. Tenths: 3+6+1=10, write 0 carry 1. Ones: 0+2+1=3. Answer: 3.015.
Adding Three or More Decimals
Pad: 1.400 + 0.350 + 2.007. Column by column right to left: thousandths 0+0+7=7; hundredths 0+5+0=5; tenths 4+3+0=7; ones 1+0+2=3. Answer: 3.757.
Mental Strategies
- Add the whole parts first, then the decimal parts: 5.3 + 2.6 = (5+2) + (0.3+0.6) = 7 + 0.9 = 7.9.
- Round-and-adjust: 3.99 + 1.5 ≈ 4 + 1.5 = 5.5, then subtract 0.01 = 5.49.
Key Takeaways
- Line up decimal points before adding.
- Pad with trailing zeros so columns match.
- Add right to left and carry just like with whole numbers.
- The decimal point in the answer is directly below the decimal points in the question.