Dividing Decimals by 10, 100 and 1000
Divide a decimal by exactly 10, 100 or 1000 with one shortcut: move the decimal point to the left! (To divide by 20, 300, 8000 and the like, see Dividing Decimals by Tens, Hundreds and Thousands.)
1. Recall: Dividing Decimals by Whole Numbers
Quick Review:
Before we learn the shortcut for dividing by 10, 100, and 1000, let's recall basic decimal division.
Example: 0.6 ÷ 2
6 tenths ÷ 2 = 3 tenths
0.6 ÷ 2 = 0.3
Example: 1.5 ÷ 3
Think: 1 one = 10 tenths, so 1.5 = 15 tenths
15 tenths ÷ 3 = 5 tenths = 0.5
1.5 ÷ 3 = 0.5
2. Dividing by 10, 100, and 1000
The Opposite Pattern:
When dividing by 10, 100, or 1000, move the decimal point to the LEFT!
(This is the opposite of multiplying by 10, 100 or 1000, where we move it RIGHT)
÷ 10
Move the decimal point 1 place LEFT
÷ 100
Move the decimal point 2 places LEFT
÷ 1000
Move the decimal point 3 places LEFT
Example: 12.4 ÷ 10
| Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|
| 1 | 2 | . | 4 | - |
| ↓ ÷ 10 (each digit moves 1 place to the right, the same as moving the decimal point 1 place LEFT) | ||||
| - | 1 | . | 2 | 4 |
12.4 ÷ 10 = 1.24
Example: 12.4 ÷ 100
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 1 | 2 | . | 4 | - | - |
| ↓ ÷ 100 (each digit moves 2 places to the right, the same as moving the decimal point 2 places LEFT) | |||||
| - | 0 | . | 1 | 2 | 4 |
12.4 ÷ 100 = 0.124
Note: We add a leading zero (0.) because the number becomes less than 1
Example: 1.3 ÷ 10
| Ones | . | Tenths | Hundredths |
|---|---|---|---|
| 1 | . | 3 | - |
| ↓ ÷ 10 (each digit moves 1 place to the right, the same as moving the decimal point 1 place LEFT) | |||
| 0 | . | 1 | 3 |
1.3 ÷ 10 = 0.13
Multiplying vs Dividing by 10, 100 or 1000
× 10, 100 or 1000
Move decimal point RIGHT →
Number gets BIGGER
÷ 10, 100 or 1000
Move decimal point ← LEFT
Number gets SMALLER
Quick Reference
÷ 10
Move decimal point
← 1 place left
÷ 100
Move decimal point
←← 2 places left
÷ 1000
Move decimal point
←←← 3 places left
Practice Problems
Practice 1: Divide by 10
Calculate: 45.6 ÷ 10
ShowHide solution
Move decimal point 1 place left: 45.6 → 4.56
Practice 2: Divide by 100
Calculate: 7.5 ÷ 100
ShowHide solution
Move decimal point 2 places left: 7.5 → 0.75 → 0.075
(There are not enough digits to move past, so we write zeros: 7.5 becomes 0.075)
Practice 3: Divide by 1000
Calculate: 234 ÷ 1000
ShowHide solution
A whole number has its decimal point at the end (234 = 234.0). Move it 3 places left: 234 → 23.4 → 2.34 → 0.234
Practice 4: Challenge
Calculate: 20.02 ÷ 10
ShowHide solution
Move decimal point 1 place left: 20.02 → 2.002
Key Takeaways
- Dividing by 10: Move decimal point 1 place left
- Dividing by 100: Move decimal point 2 places left
- Dividing by 1000: Move decimal point 3 places left
- Add leading zeros (e.g., 0.075) when the number becomes less than 1
- Dividing by 10, 100 or 1000 makes a number smaller, so the decimal point moves LEFT