Dividing by 10, 100 and 1,000
Learn the patterns for dividing a whole number by exactly 10, 100 or 1,000. (To divide by numbers such as 30, 400 or 5,000, see Dividing by Tens, Hundreds and Thousands.)
1. Dividing by 10
The Pattern
When a whole number ends in zero, dividing it by 10 removes one zero from the end.
This is the opposite of multiplying by 10!
Examples:
10 ÷ 10 = 1
Because 1 × 10 = 10
100 ÷ 10 = 10
Because 10 × 10 = 100
320 ÷ 10 = 32
32,000 ÷ 10 = 3,200
Why does this work?
When you divide by 10, each digit moves one place to the right in the place value chart. The zero at the end disappears!
2. Dividing by 100
The Pattern
When a whole number ends in two zeros (or more), dividing it by 100 removes two zeros from the end.
Examples:
100 ÷ 100 = 1
Because 1 × 100 = 100
32,000 ÷ 100 = 320
5,900 ÷ 100 = 59
245,000 ÷ 100 = 2,450
3. Dividing by 1,000
The Pattern
When a whole number ends in three zeros (or more), dividing it by 1,000 removes three zeros from the end.
Examples:
32,000 ÷ 1,000 = 32
59,000 ÷ 1,000 = 59
245,000 ÷ 1,000 = 245
Summary: Division Patterns
| Divide | 32,000 |
|---|---|
| ÷ 10 | 3,200 |
| ÷ 100 | 320 |
| ÷ 1,000 | 32 |
Division is the Opposite of Multiplication!
If 245 × 10 = 2,450, then 2,450 ÷ 10 = 245
If 245 × 100 = 24,500, then 24,500 ÷ 100 = 245
If 245 × 1,000 = 245,000, then 245,000 ÷ 1,000 = 245
Practice Problems
Find the quotients:
a) 590 ÷ 10 = ?
b) 7,300 ÷ 100 = ?
c) 46,000 ÷ 1,000 = ?
d) 480,000 ÷ 100 = ?
e) 7,000,000 ÷ 1,000 = ?
ShowHide solutions
a) 590 ÷ 10 = 59 (remove 1 zero)
b) 7,300 ÷ 100 = 73 (remove 2 zeros)
c) 46,000 ÷ 1,000 = 46 (remove 3 zeros)
d) 480,000 ÷ 100 = 4,800 (remove 2 zeros)
e) 7,000,000 ÷ 1,000 = 7,000 (remove 3 zeros)
Key Takeaways
- ÷ 10: Digits move right 1 place, so a whole number ending in zero loses ONE zero from the end
- ÷ 100: Digits move right 2 places, so a whole number ending in two zeros loses TWO zeros
- ÷ 1,000: Digits move right 3 places, so a whole number ending in three zeros loses THREE zeros
- Division is the inverse (opposite) of multiplication
- You can check your answer by multiplying back!