Decimal × Decimal

1Summary 重點摘要

0.2 × 0.3 = 0.06.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Multiply as whole numbersFor 0.2 × 0.3, ignore the decimal points at first and multiply 2 × 3 = 6 as whole numbers. Getting the digits right comes first; the point is placed afterwards. This keeps your attention on the multiplication itself.
2. Step 2: Count the decimal placesCount the decimal places of both factors: 0.2 has 1 place and 0.3 has 1 place, so together there are 2 places. The product always has as many decimal places as both factors put together, so remember this total.
3. Step 3: Place the point from the rightCount 2 places from the right of the product 6 and write the point: 0.06. If the digits run out, pad zeros on the left: with 3 places, the 6 becomes 0.006. Padding keeps the counting accurate.
4. Step 4: Why the product is smaller0.2 means 210 and 0.3 means 310, so the product is 6100, which is 0.06. Multiplying two numbers smaller than 1 gives a result smaller than both, which is quite different from whole-number multiplication.
5. Step 5: Estimate to check0.2 × 0.3 must be smaller than both 0.2 and 0.3. An answer like 0.6 or 6 is impossible, because the product cannot exceed either factor. A quick size check catches a misplaced decimal point early.
6. Step 6: More decimal placesTry a longer example: 1.2 × 0.15. As whole numbers, 12 × 15 = 180; the places total 1 + 2 = 3, so count 3 from the right to get 0.180, and the trailing zero can be dropped: the answer is 0.18.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Multiply as whole numbers first, then place the point
• Total decimal places = places of both factors added
• Pad zeros from the right when needed (0.3 × 0.02 = 0.006)
• Multiplying by a number under 1 makes the value smaller
• Always sanity-check with an estimate