Multiplying by 10, 100 and 1,000
Learn the patterns for multiplying a whole number by exactly 10, 100 or 1,000. (To multiply by numbers such as 30, 400 or 5,000, see Multiplying by Tens, Hundreds and Thousands.)
1. Multiplying by 10
The Pattern
When you multiply a whole number by 10, you write one zero at the end.
Examples:
1 × 10 = 10
3 × 10 = 30
12 × 10 = 120
245 × 10 = 2,450
728 × 10 = 7,280
8,990 × 10 = 89,900
Why does this work?
When you multiply by 10, each digit moves one place to the left in the place value chart. The empty ones place gets filled with a zero. This shortcut is for whole numbers only: for 2.5 × 10, the digits move one place to the left to give 25, not 2.50.
2. Multiplying by 100
The Pattern
When you multiply a whole number by 100, you write two zeros at the end.
This makes sense because 100 = 10 × 10, so × 100 = × 10 × 10
Examples:
1 × 100 = 100
3 × 100 = 300
12 × 100 = 1,200
27 × 100 = 2,700
245 × 100 = 24,500
4,992 × 100 = 499,200
3. Multiplying by 1,000
The Pattern
When you multiply a whole number by 1,000, you write three zeros at the end.
This makes sense because 1,000 = 10 × 10 × 10, so × 1,000 = × 10 × 10 × 10
Examples:
3 × 1,000 = 3,000
12 × 1,000 = 12,000
165 × 1,000 = 165,000
245 × 1,000 = 245,000
Summary Pattern
| Multiply by | 3 | 12 | 245 |
|---|---|---|---|
| × 10 | 30 | 120 | 2,450 |
| × 100 | 300 | 1,200 | 24,500 |
| × 1,000 | 3,000 | 12,000 | 245,000 |
Practice Problems
1. Multiply:
a) 14 × 10 = ?
b) 506 × 10 = ?
c) 83 × 100 = ?
d) 240 × 1,000 = ?
ShowHide solutions
a) 14 × 10 = 140 (write 1 zero at the end)
b) 506 × 10 = 5,060 (write 1 zero at the end)
c) 83 × 100 = 8,300 (write 2 zeros at the end)
d) 240 × 1,000 = 240,000 (write 3 zeros at the end)
2. Raju and Xinyi noticed that 7 × 100 = 7 × 10 × 10. Write 7 × 1,000 in the same way, then find its value.
ShowHide solution
7 × 1,000 can be written as:
7 × 1,000 = 7 × 10 × 10 × 10 = 7,000
We can also write it as:
7 × 1,000 = 7 × 10 × 100 = 70 × 100 = 7,000
Key Takeaways
- × 10: Write ONE zero at the end of a whole number (digits move left 1 place)
- × 100: Write TWO zeros at the end of a whole number (digits move left 2 places)
- × 1,000: Write THREE zeros at the end of a whole number (digits move left 3 places)
- 100 = 10 × 10, so × 100 = × 10 × 10
- 1,000 = 10 × 10 × 10, so × 1,000 = × 10 × 10 × 10