Multiplication of Positive Decimal Fractions
Multiply decimals as whole numbers, then place the decimal point
Key Idea
Multiply decimal fractions as if they were whole numbers, then place the decimal point in the product. Count the total number of decimal places in both factors — the answer has exactly that many digits after the decimal point!
The Main Rule
Algorithm for multiplying decimals:
- Step 1: Ignore the decimal points and multiply the numbers as whole numbers
- Step 2: Count the digits after the decimal point in the first factor
- Step 3: Count the digits after the decimal point in the second factor
- Step 4: Add these two counts
- Step 5: Count that many digits from right to left in the product and place the decimal point
Formula: Decimal places in the product = places in the 1st factor + places in the 2nd factor
Visualizing the Rule
Interactive visualization — available in the full lesson
When Leading Zeros Are Needed
Example: 0.02 × 0.3
- Multiply: 2 × 3 = 6
- Count the places: 2 + 1 = 3
- The number 6 has only one digit, but we need 3 decimal places
- Add zeros on the left: 0.006
- Answer: 0.006
Remember!
If the product has fewer digits than the required number of decimal places, add zeros to the left of the number (right after the decimal point).
Example: 3 places are needed and the number is 6 → write 0.006