Multiplying decimals uses a fact you already know — how to multiply whole numbers — plus one new skill: figuring out exactly where the decimal point belongs in your answer.
Here's the trick: ignore the decimal points at first and multiply the numbers as if they were whole numbers. Once you have that answer, come back and figure out where the decimal point goes.
To know where the point goes, count the total number of decimal places in both factors combined. 0.4 has 1 decimal place, and 0.3 has 1 decimal place, so the answer needs 1 + 1 = 2 decimal places. Starting from the right side of 12, count 2 digits over — that's where the point goes:
Try 0.2 × 0.3: ignoring the points, 2 × 3 = 6. That needs 2 decimal places, but "6" only has one digit. Counting 2 places from the right runs off the end of the number — so add a zero in front to make room, then place the point:
The number of decimal places in your answer is always the sum of the decimal places in the two factors — no matter how big or small the whole-number product turns out to be.
| Problem | Places in each factor | Total places in answer |
|---|---|---|
| 3.2 × 0.05 | 1 + 2 | 3 |
| 1.5 × 2.4 | 1 + 1 | 2 |
| 0.06 × 0.7 | 2 + 1 | 3 |
Before placing the point, round each factor and estimate: 3.2 × 0.05 is close to 3 × 0.05 = 0.15 — a small number. If your placed answer looks wildly different from your estimate, you probably put the point in the wrong spot.
Work through each problem in two stages: first count the decimal places, then place the point to get the final answer.
Here's the problem, multiplied as if there were no decimal points.