Multiplying a Decimal by a Whole Number

4 × 0.3 is 4 groups of 3 tenths, which is 12 tenths.

Then say what that is

12 tenths is 1 whole and 2 tenths, written 1.2.

Hundredths work the same

3 × 0.25 is 3 groups of 25 hundredths, which is 75 hundredths, or 0.75.

Check the size

4 × 0.3 should be near 4 × 0.3, so around 1. An answer of 12 would be wrong.

Count in the decimal's unit

4 × 0.3 is four lots of three tenths, which is twelve tenths, which is 1.2. Working in the named unit — tenths — makes the calculation into ordinary whole-number multiplication with a label attached at the end.

The practical method

Multiply as if there were no decimal point, then put the point back so the answer has as many decimal places as the original decimal had. For 4 × 0.3: 4 × 3 = 12, one decimal place, so 1.2. The counting-in-tenths argument is why this works.

Estimate to place the point

4 × 0.3 should be a bit more than 1, since 0.3 is roughly a third and four thirds is a bit over one. That tells you the answer is 1.2 rather than 12 or 0.12. Estimating is the most reliable way to place a decimal point.

Money makes it concrete

Four items at $0.30 each cost $1.20. You can check this by counting coins. Whenever a decimal multiplication feels abstract, recast it as money — the arithmetic is identical and the answer becomes something you can verify physically.