Example 1 · Scale the whole-number product
Calculate \(2.4\times1.3\).
Show the reasoning
\[24\times13=312,\qquad 2.4\times1.3=\frac{312}{100}=3.12.\]Because \(1.3>1\), the answer should be greater than \(2.4\).
Year 7 · Decimals
Multiplying decimals
Multiply decimals using place value and explain when a product becomes smaller.
8 questions in the first lesson. Allow about 10–15 minutes at your own pace. More short sets are available below.
Understand the method
First multiply the whole-number digits. Then use place value to scale the product. For example, \(2.4=\frac{24}{10}\) and \(1.3=\frac{13}{10}\), so their product is \(\frac{24\times13}{100}\).
Count the decimal places in both factors together. Preserve zero placeholders when a product is less than one.
For a positive starting value, multiplication by a positive number below one makes the result smaller. Multiplication by one keeps it equal. Use this to check the size of an answer.
Worked examples
Example 2 · Keep zero placeholders
Calculate \(0.48\times0.06\).
Show the reasoning
\[48\times6=288,\qquad 0.48\times0.06=\frac{288}{10000}=0.0288.\]There are four decimal places altogether. Both factors are below one, and the product is smaller than either factor.
Check your method
- Counting decimal places in only one factor.
- Assuming multiplication always makes a number larger.
- Losing zeros at the start of a small decimal.
Review after a break
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Exercises include the supplied Year 7 Decimal Calculations collection. Lessons, explanations and additional understanding checks were prepared with AI assistance. Teacher review pending.