Multiplying Decimals

4 × 1.42

1Break Apart by Place

1.42 = 1 + 0.4 + 0.02

4 × 1 = 4 · 4 × 0.4 = 1.6 · 4 × 0.02 = 0.08

4 + 1.6 + 0.08 = 5.68

Four groups of each place, then add. It is the same idea as with whole numbers.

2Area Model

10.40.02

4 × 1

4 × 0.4

1.6

4 × 0.02

0.08

4 + 1.6 + 0.08 = 5.68

Each place gets its own box, so the small pieces stay visible.

3The Algorithm, to Check

1.42

× 4

5.68

Multiply as if it were 142 × 4 = 568.
1.42 has two decimal places, so the product gets two: 5.68.

Count decimal places at the end. The model shows why the point goes there.

4Estimate to Catch Mistakes

1.42 is close to 1½ → 4 × 1½ = 6

5.68 is near 6 ✓

A misplaced point gives 56.8 or 0.568, and neither is near 6.

The estimate checks the answer.