Multiplying Decimals by 10, 100 and 1000
Multiply a decimal by exactly 10, 100 or 1000 with one shortcut: move the decimal point to the right! (To multiply by 20, 300, 5000 and the like, see Multiplying Decimals by Tens, Hundreds and Thousands.)
1. Recall: Multiplying Decimals by Whole Numbers
Quick Review:
Before we learn the shortcut, let's recall how decimals work with place value.
Example: 0.3 × 3
3 tenths × 3 = 9 tenths
0.3 × 3 = 0.9
Example: 0.03 × 3
3 hundredths × 3 = 9 hundredths
0.03 × 3 = 0.09
2. Multiplying by 10
The Pattern:
When you multiply a decimal by 10, move the decimal point 1 place to the right.
Example: 0.3 × 10
| Ones | . | Tenths |
|---|---|---|
| 0 | . | 3 |
| ↓ × 10 (each digit moves 1 place to the left, the same as moving the decimal point 1 place right) | ||
| 3 | . | - |
3 tenths become 3 ones
0.3 × 10 = 3
Example: 1.25 × 10
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| - | 1 | . | 2 | 5 |
| ↓ × 10 (each digit moves 1 place to the left, the same as moving the decimal point 1 place right) | ||||
| 1 | 2 | . | 5 | - |
1.25 × 10 = 12.5
3. Multiplying by 100 and 1000
× 100
Move the decimal point 2 places to the right
× 1000
Move the decimal point 3 places to the right
Example: 1.25 × 100
| Hundreds | Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|---|
| - | - | 1 | . | 2 | 5 |
| ↓ × 100 (each digit moves 2 places to the left, the same as moving the decimal point 2 places right) | |||||
| 1 | 2 | 5 | . | - | - |
1.25 × 100 = 125
Example: 1.25 × 1000
| Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|---|---|
| - | - | - | 1 | . | 2 | 5 |
| ↓ × 1000 (each digit moves 3 places to the left, the same as moving the decimal point 3 places right) | ||||||
| 1 | 2 | 5 | 0 | . | - | - |
1.25 × 1000 = 1250
Note: We write a 0 in the ones place because we need to move 3 places but there are only 2 digits after the decimal point
📌 Quick Reference
× 10
Move decimal point
1 place right →
× 100
Move decimal point
2 places right →→
× 1000
Move decimal point
3 places right →→→
Practice Problems
Practice 1: Multiply by 10
Calculate: 0.41 × 10
ShowHide solution
Move decimal point 1 place right: 0.41 → 4.1
Practice 2: Multiply by 100
Calculate: 0.41 × 100
ShowHide solution
Move decimal point 2 places right: 0.41 → 41
Practice 3: Multiply by 1000
Calculate: 0.41 × 1000
ShowHide solution
Move decimal point 3 places right: 0.41 → 4.1 → 41 → 410
(Write a 0 in the ones place because we need to move 3 places but there are only 2 digits after the decimal point)
Practice 4: With Thousandths
Calculate: 2.002 × 100
ShowHide solution
Move decimal point 2 places right: 2.002 → 200.2
Key Takeaways
- Multiplying by 10: Move decimal point 1 place right
- Multiplying by 100: Move decimal point 2 places right
- Multiplying by 1000: Move decimal point 3 places right
- If you run out of digits, add zeros as needed
- The digits stay in the same order - only their places change