Multiplying and Dividing Decimals

Multiply as whole numbers, then place the point. 0.3 × 0.4 uses 3 × 4 = 12, giving 0.12.

Counting the places

0.3 has one place and 0.4 has one, so the answer has two: 0.12.

Dividing by a decimal

Scale both numbers by 10 until the divisor is whole. 6 ÷ 0.2 becomes 60 ÷ 2 = 30.

Always check the size

0.3 × 0.4 must be less than either, since both factors are under 1.

Counting decimal places

Multiply as if the points were not there, then give the answer as many decimal places as the two factors had between them. 0.3 × 0.4: 3 × 4 = 12, two decimal places, so 0.12. The rule follows from place value, not from convention.

The size check matters more than the rule

0.3 × 0.4 must be smaller than either factor, since both are less than one. 0.12 fits; 1.2 or 12 would not. Whenever the place-counting rule feels uncertain, decide the rough size first and let that place the point.

Dividing: scale both up

For 1.44 ÷ 0.12, multiply both by 100 to get 144 ÷ 12 = 12. Scaling both numbers by the same factor leaves the quotient unchanged, and it converts every decimal division into a whole-number one.

Dividing by less than one enlarges

1.44 ÷ 0.12 = 12, much bigger than 1.44. This still surprises people. Reading it as "how many 0.12s fit into 1.44" makes the answer obviously reasonable, and that reading is the best defence against a misplaced point.