Dividing Decimals by Tens, Hundreds and Thousands
Learn to divide decimals by 20, 30, 200, 600, 8000 and more: divide by the single digit, then by 10, 100 or 1000. (For dividing by 10, 100 or 1000 alone, see Dividing Decimals by 10, 100 and 1000.)
1. The Decomposition Strategy for Division
Key Idea:
Just like multiplication, break down the divisor into smaller parts:
- 20 = 2 × 10 → Divide by 2, then divide by 10
- 30 = 3 × 10 → Divide by 3, then divide by 10
- 400 = 4 × 100 → Divide by 4, then divide by 100
- 8000 = 8 × 1000 → Divide by 8, then divide by 1000
💡 Remember: You can do the two divisions in either order. For 30: ÷ 3 then ÷ 10, or ÷ 10 then ÷ 3. Here we divide by the single digit first, then by 10, 100, or 1000.
2. Dividing by Tens (20, 30, 40...)
Example: 6.3 ÷ 30
Think: 30 = 3 × 10
So: 6.3 ÷ 30 = 6.3 ÷ 3 ÷ 10
6.3 ÷ 30 = 0.21
Example: 8.16 ÷ 20
Think: 20 = 2 × 10
So: 8.16 ÷ 20 = 8.16 ÷ 2 ÷ 10
8.16 ÷ 20 = 0.408
Alternative method:
Same answer either way!
3. Dividing by Hundreds (200, 400, 600...)
Example: 100.4 ÷ 400
Think: 400 = 4 × 100
So: 100.4 ÷ 400 = 100.4 ÷ 4 ÷ 100
100.4 ÷ 400 = 0.251
Example: 72 ÷ 600
Think: 600 = 6 × 100
So: 72 ÷ 600 = 72 ÷ 6 ÷ 100
72 ÷ 600 = 0.12
4. Dividing by Thousands (2000, 8000...)
Example: 208 ÷ 8000
Think: 8000 = 8 × 1000
So: 208 ÷ 8000 = 208 ÷ 8 ÷ 1000
208 ÷ 8000 = 0.026
Example: 9084 ÷ 3000
Think: 3000 = 3 × 1000
So: 9084 ÷ 3000 = 9084 ÷ 3 ÷ 1000
9084 ÷ 3000 = 3.028
📌 The Decomposition Method for Division
Step 1: Break down the divisor
20 = 2 × 10
40 = 4 × 10
400 = 4 × 100
600 = 6 × 100
2000 = 2 × 1000
8000 = 8 × 1000
Step 2: Divide by the single digit first
Step 3: Then divide by 10, 100, or 1000 (move the decimal point LEFT)
Practice Problems
Practice 1: Divide by Tens
Calculate: 188 ÷ 40
ShowHide solution
40 = 4 × 10
Step 1: 188 ÷ 4 = 47
Step 2: 47 ÷ 10 = 4.7
Practice 2: Divide by Tens
Calculate: 0.64 ÷ 20
ShowHide solution
20 = 2 × 10
Step 1: 0.64 ÷ 2 = 0.32
Step 2: 0.32 ÷ 10 = 0.032
Practice 3: Divide by Hundreds
Calculate: 6 ÷ 200
ShowHide solution
200 = 2 × 100
Step 1: 6 ÷ 2 = 3
Step 2: 3 ÷ 100 = 0.03
Practice 4: Divide by Thousands
Calculate: 84 ÷ 2000
ShowHide solution
2000 = 2 × 1000
Step 1: 84 ÷ 2 = 42
Step 2: 42 ÷ 1000 = 0.042
Key Takeaways
- Break down the divisor: 30 = 3 × 10, 400 = 4 × 100, etc.
- Divide by the single digit first, then by 10, 100, or 1000
- You can do the two divisions in either order - the answer is the same!
- When dividing by 10, 100 or 1000, move the decimal point LEFT
- Add leading zeros when needed (e.g., 0.032)