Decimal multiplication 0.4 × 0.3 grid — free printable diagram

How the grid shows 0.4 × 0.3 = 0.12

A 10 × 10 grid stands for one whole, so each of its 100 small squares is one hundredth, 0.01. Shading 4 columns gives 0.4 and shading 3 rows gives 0.3; the 12 squares where they overlap are the answer, 0.12.

Calculation

0.4 × 0.3

Answer

0.12

The grid

10 × 10 = 100 small squares

Each small square

0.01 — one hundredth of the whole

Columns shaded

4, which is 0.4

Rows shaded

3, which is 0.3

Squares in the overlap

4 × 3 = 12

The answer as a fraction

12/100 = 3/25

• The quick method is the same arithmetic without the picture: multiply 4 × 3 = 12, then count the decimal places. 0.4 has one and 0.3 has one, so the answer has two — 12 hundredths, which is 0.12.
• The answer being smaller than both numbers you started with is the part that looks wrong and is not. Multiplying by 0.3 means taking 0.3 of something, and 0.3 is less than one whole, so the result has to be less than 0.4. On the grid you can see it: the overlap is a part of the 4 shaded columns, not more than them.
• Reading the grid as fractions says the same thing: 4/10 × 3/10 = 12/100. Multiplying tenths by tenths gives hundredths, because the squares are tenths of tenths.