Multiply decimals by whole numbers
Theory
To multiply a decimal by a whole number, you can count tenths or hundredths, or multiply as if there were no decimal point and then put the point back so the answer has the same number of decimal places. Always check with an estimate. This Year 6 maths page shows each method with money and measurement examples.
Multiplying is repeated addition: \(0.4 \times 3 = 0.4 + 0.4 + 0.4 = 1.2\).
Think in place value units: \(0.06\) is \(6\) hundredths, so \(0.06 \times 7\) is \(42\) hundredths \(= 0.42\).
Written method: ignore the point and multiply the whole numbers (\(365 \times 6 = 2190\)), then put the point back with the same number of decimal places as the decimal (\(3.65 \times 6 = 21.90\)).
Estimate to check the point: \(3.65 \times 6 \approx 4 \times 6 = 24\), so \(21.90\) is sensible.
Multiplying by a number less than \(1\) makes the answer smaller: \(0.5 \times 90 = 45\).
Multiplying decimals by whole numbers:
Written method
- Estimate by rounding the decimal to a whole number.
- Multiply the digits as whole numbers.
- Count the decimal places in the decimal and give the answer the same number.
- Check the answer is close to the estimate.
| \(0.4 + 0.4 + 0.4\) | \(=\) | \(1.2\) |
\(1.2\).
| \(6 \times 7\) | \(=\) | \(42\ \text{hundredths}\) |
\(0.42\).
| \(2 \times 4 + 0.3 \times 4\) | \(=\) | \(8 + 1.2\) |
| \(8 + 1.2\) | \(=\) | \(9.2\) |
\(9.2\).
| \(365 \times 6\) | \(=\) | \(2190\) |
| \(3.65 \times 6\) | \(=\) | \(21.90\) |
\(21.9\). Estimate: \(4 \times 6 = 24\). Sensible.
| \(485 \times 3\) | \(=\) | \(1455\) |
| \(4.85 \times 3\) | \(=\) | \(14.55\) |
\(\$14.55\).
| \(0.25 \times 12\) | \(=\) | \(3\) |
\(0.25\) is a quarter, and \(12\) quarters make \(3\) wholes.
| \(1.75 \times 8\) | \(=\) | \(14\) |
\(14\) m.
| \(7 \times 4\) | \(=\) | \(28\) |
The estimate is \(28\), so \(27.6\).
Common pitfalls
Frequently asked questions
How do I multiply a decimal by a whole number?
Multiply as whole numbers, then give the answer the same number of decimal places: \(3.65 \times 6 = 21.90\).
What is 0.4 × 3?
\(1.2\).
How do I know where the decimal point goes?
Count decimal places, and check with an estimate.
Can multiplying make a number smaller?
Yes, if you multiply by a number less than \(1\): \(0.5 \times 90 = 45\).
How do I check the answer?
Round the decimal to a whole number: \(6.9 \times 4 \approx 7 \times 4 = 28\).