All From 9, Last From 10: The Fastest Way to Subtract From Powers of Ten

The Problem With Ordinary Subtraction

Subtracting a number from 1000, 10000, or any power of ten the standard way usually means borrowing across several zeros — a step where many students make mistakes. The "All from 9, Last from 10" rule removes borrowing entirely.

The Rule

• Line up the number you're subtracting so it has as many digits as the power of ten has zeros (pad with leading zeros if needed).
• Subtract every digit except the last one from 9.
• Subtract the last digit from 10.
• Read off the digits in order — that's your answer.

Worked Example

1000 − 587

1. Digits of 587: 5, 8, 7
2. All digits except the last, from 9: 9 − 5 = 4, and 9 − 8 = 1
3. Last digit, from 10: 10 − 7 = 3
4. Answer: 413

A Bigger Example

10000 − 4321

1. Digits: 4, 3, 2, 1
2. From 9 (all but last): 9 − 4 = 5, 9 − 3 = 6, 9 − 2 = 7
3. From 10 (last digit): 10 − 1 = 9
4. Answer: 5679

A Shorter Example

100 − 47

1. Pad to two digits: 4, 7
2. From 9: 9 − 4 = 5
3. From 10: 10 − 7 = 3
4. Answer: 53

Why It Works

A power of ten like 1000 can be thought of as 999 + 1. Subtracting a number from 999 never needs borrowing, since every digit of 999 is 9. So "all from 9" handles the 999 part, and the leftover "+1" is exactly what turns the last digit's subtraction from 9 into subtraction from 10.

Where Students Go Wrong

• Forgetting to pad with leading zeros when the number being subtracted has fewer digits than the power of ten has zeros (for example, treating 100 − 7 the same as 100 − 47).
• Applying "from 10" to more than just the last digit.

Practice Tip

Pick a power of ten and subtract five different numbers from it using this rule, then verify one or two with standard subtraction. Once the pattern is automatic, subtracting from powers of ten becomes a glance-and-write calculation rather than a multi-step borrowing exercise — extremely useful whenever a timed test throws a "difference from 1000" style question at you.