Example 1 · Count tenths
3.8 ÷ 0.1 = 38. A whole contains 10 tenths, so 3 wholes contain 30 tenths. Add the remaining 8 tenths: 38 tenths.
Mathematics · Decimals · Topic 11 · 4 of 5
Mental Division by 10, 100, 1,000 and Small Decimals
Use place value to divide by 0.1, 0.01, 0.001, 10, 100, and 1,000.
Think about place value
When a positive number is divided by 10, each digit’s value becomes one tenth as large. When it is divided by 0.1, you are counting how many tenths fit inside it.
| Divide by | Equivalent operation | Example with 4.08 |
|---|---|---|
| 10 | Move decimal left 1 place | 0.408 |
| 100 | Move decimal left 2 places | 0.0408 |
| 1,000 | Move decimal left 3 places | 0.00408 |
| 0.1 | Multiply by 10 | 40.8 |
| 0.01 | Multiply by 100 | 408 |
| 0.001 | Multiply by 1,000 | 4,080 |
Example 2 · Keep the zeros
0.086 ÷ 0.001 = 86. There are 86 thousandths in 0.086.
0.965 ÷ 1,000 = 0.000965. Move left three places and insert zeros as placeholders.
Example 3 · Use the rule in a problem
A 2.8 m ribbon is cut into pieces of 0.1 m. Calculate 2.8 ÷ 0.1 = 28 pieces.
Quick check: Dividing by 100 makes a positive number smaller; dividing by 0.01 makes it larger. The directions are opposites.