Subtracting Decimals – Align, Borrow, and Subtract
Subtracting decimals follows the same column-by-column approach as subtracting whole numbers. Line up the decimal points, borrow when needed, and keep the decimal point in the answer directly below those in the question.
Borrowing across a decimal point works exactly like borrowing across any other column boundary in whole-number subtraction — the only extra care needed is padding both numbers to the same number of decimal places first, so there is never any ambiguity about which column is which. This shows up constantly with money: working out change from a banknote (10.00 − 6.49) always involves borrowing through several zero columns, which is precisely why cashiers are trained to count change upward instead (adding from 6.49 back to 10.00) rather than subtracting directly.
The Method
1. Line up the decimal points.
2. Pad with trailing zeros if the numbers have different lengths.
3. Subtract right to left, borrowing from the next column when the top digit is smaller than the bottom digit.
4. Place the decimal point in the answer directly below.
Try It: 15.2 − 6.45
Pad 15.2 to 15.20, then subtract right to left — borrowing carries all the way across the decimal point into the ones and tens columns.
Simple Subtraction
Tenths: 7-4=3. Ones: 8-3=5. Answer: 5.3.
Pad 1.8 as 1.80.
Hundredths: 2 − 0 = 2.
Tenths: 5 − 8 — not enough, so borrow 1 from the ones column. Ones drop from 6 to 5, and the tenths digit becomes 15: 15 − 8 = 7.
Ones: 5 − 1 = 4.
Answer: 4.72.
Subtraction with Borrowing
Pad 12.3 as 12.30.
Hundredths: 0 − 5 — borrow 1 from the tenths column (3 becomes 2): 10 − 5 = 5.
Tenths: 2 − 7 — borrow 1 from the ones column (2 becomes 1): 12 − 7 = 5.
Ones: 1 − 4 — borrow 1 from the tens column (1 becomes 0): 11 − 4 = 7.
Tens: 0 − 0 = 0 (no digit needed).
Answer: 7.55.
Write 5 as 5.00.
Hundredths: 0 − 7 — borrow 1 from the tenths column, but the tenths digit is also 0, so first borrow 1 from the ones column (5 becomes 4) making the tenths digit 10; now borrow 1 from that 10 for the hundredths (tenths becomes 9): 10 − 7 = 3.
Tenths: 9 − 3 = 6.
Ones: 4 − 1 = 3.
Answer: 3.63.
Checking by Addition
You can always check a subtraction by adding your answer back to the number you subtracted. 3.63 + 1.37 should equal 5. Let us verify: 3.63 + 1.37 = 5.00. Correct.
Real-Life Examples
- Change from £10.00 after spending £6.49: 10.00 - 6.49 = £3.51.
- Rainfall difference: 34.7 mm last month vs 29.85 mm this month. Difference = 4.85 mm.
- Temperature drop from 15.2°C to 8.75°C = 6.45°C decrease.
Key Takeaways
- Align decimal points before subtracting.
- Add trailing zeros so columns match.
- Borrow from the next column when needed, exactly as with whole numbers.
- Check your answer by adding result to the subtracted value.