Multiplying decimals — Mathematics, 11–13
Multiply as if there were no decimal points, then put the point back: the product has as many decimal places as both factors together.
Times a tenth is taking a tenth
Multiplying by 0.1 is multiplying by 1/10, that is, taking a tenth: 45 × 0.1 = 4.5. Multiplying by 0.01 (1/100) takes a hundredth: 45 × 0.01 = 0.45; by 0.001 (1/1000): 45 × 0.001 = 0.045. For other decimals, multiply as if they were natural numbers, then count the decimal places of the factors: 0.3 × 0.2 → 3 × 2 = 6, and 1 + 1 = 2 places, so 0.06.
Why the places add up
0.3 is 3 tenths and 0.2 is 2 tenths. A tenth of a tenth is a hundredth, so 3 × 2 = 6 gives 6 hundredths: 0.06. The decimal places add up because each factor brings its own size of parts. You can also see it in an area: a rectangle 0.3 m by 0.2 m has an area of 0.06 m².
2.4 × 1.5, step by step
Work out 2.4 × 1.5. Step 1: forget the decimal points and multiply: 24 × 15 = 360. Step 2: count the decimal places of the factors: 2.4 has 1 and 1.5 has 1, so 2 in total. Step 3: put the point so that the product has 2 places: 3.60, which is 3.6. Check: 2 × 1.5 = 3 and 2.4 is a bit more than 2, so a value a little above 3 makes sense.
0.3 × 0.2 is not 0.6
A common mistake is writing 0.3 × 0.2 = 0.6, because 3 × 2 = 6 and “one digit after the point is enough”. But there are 1 + 1 = 2 decimal places, so the product is 0.06. A way to doubt 0.6: 0.2 is less than 1, so 0.3 × 0.2 is smaller than 0.3, and 0.6 is not. Note that a zero on the right can disappear: 0.5 × 0.2 = 0.10 = 0.1.
Areas and quantities
Multiplying decimals appears in areas and quantities. A table 1.2 m by 0.8 m has an area of 1.2 × 0.8 = 0.96 m², because 12 × 8 = 96 and there are 2 places. If one packet holds 0.25 kg of rice, 3 packets hold 3 × 0.25 = 0.75 kg (3 × 25 = 75, 2 places). A natural number has 0 decimal places, so only the ones of the decimal count.
Keep exploring
Other languages
Loading MyLeoNes™…