Multiplying decimals
Connect decimal multiplication to whole-number products and powers of ten.
Before you begin
- Whole-number multiplication
- Decimal place value
Track the size of the units
Think of 1.2 × 0.3 as twelve tenths times three tenths. Twelve times three is 36, and a tenth times a tenth is a hundredth, giving 36 hundredths. This explains the usual method: multiply as whole numbers, then account for the combined decimal places. The decimal placement comes from the size of the units, not from lining up decimal points.
Use magnitude as a check
Multiplication does not always make a positive number larger. A multiplier between zero and one selects a fraction of the original quantity. For example, half of a length is shorter than the length. Estimate with simple fractions or rounded values before calculating. An answer for 0.4 × 8 must be below 8, whereas 4 × 8 is above 8.
Worked example
Find the cost of 2.4 kg of rice priced at $1.35 per kg.
Show the worked solution
- Multiply the whole-number digits: 24 × 135 = 3,240.
- The factors have three decimal places in total, so the product is 3.240.
- The cost is $3.24. It is between the cost of 2 kg and 3 kg, as expected.
$3.24.
Try it yourself
Which product equals 0.042?
Common mistakes
- Multiplying positive numbers by a factor below one makes them smaller.
- Use square units for an area, even when the numerical answer is a whole number.
What can you explain now?
Calculate the area of a rectangle 1.25 m long and 0.8 m wide.
Compare with the explanation
1 m².
125 × 8 = 1,000. Dividing by 1,000 gives 1.000. Area combines two lengths, so the unit is square metres.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗