What Is Multiplying by Powers of Ten?
Multiplying by 10, 100, or 1000 is the simplest mental multiplication because it only requires shifting digits. Multiply by 10: append one zero. Multiply by 100: append two zeros. Multiply by 1000: append three zeros. For decimals, move the decimal point right instead.
Why This Skill Is Essential
Powers of ten appear constantly: converting units (meters to centimeters), calculating percentages (which are based on ÷100), scaling recipes, and understanding scientific notation. This technique also forms the basis for more advanced tricks like multiplying by 5 (×10 ÷2) and multiplying by 25 (×100 ÷4).
The Place Value Rule
Each power of ten shifts every digit one place left in the number system. Multiplying by 10 moves the ones digit to tens, tens to hundreds, and so on. This is why 47 × 10 = 470 — the 4 moves from tens to hundreds, the 7 from ones to tens, and a zero fills the ones place.
For decimals, the same rule applies in reverse direction. 5.2 × 100: move the decimal two places right → 520. If you run out of digits, add zeros: 0.45 × 1000 = 450.
Building on This Foundation
Once multiplying by 10/100/1000 is automatic, you can derive other shortcuts. Multiply by 5 = multiply by 10, then halve. Multiply by 50 = multiply by 100, then halve. Multiply by 25 = multiply by 100, then divide by 4. These derived tricks multiply your mental math speed dramatically.
Practice Examples
Example 1: 47 × 10 = ?
- Append one zero to 47
- Answer: 470
Answer: 470
Example 2: 36 × 100 = ?
- Append two zeros to 36
- Answer: 3,600
Answer: 3,600
Example 3: 5.2 × 1000 = ?
- Move decimal point 3 places right
- 5.2 → 52 → 520 → 5,200
Answer: 5,200