Multiplying with Decimals
Every question with a fully worked solution.
- Multiplying with Decimals - Video - Multiply a Decimal by a Decimal Watch
Theory
To multiply decimals, multiply the numbers without the decimal points, then count the decimal places in the question to put the point back in. The total number of decimal places in the question equals the number in the answer. This Year 7 maths page shows why this works and how to use it for money, areas and longer products.
Step 1. Multiply without the decimal points. For \(0.6 \times 0.04\), work out \(6 \times 4 = 24\).
Step 2. Count the decimal places in both numbers: \(0.6\) has \(1\) and \(0.04\) has \(2\), so the answer has \(1 + 2 = 3\).
Step 3. Put the point in: \(3\) places means \(\div 1000\), so \(24 \div 1000 = 0.024\). Write zeros in front when there are not enough digits.
Why it works: tenths times tenths make hundredths. \(0.6 \times 0.4\) is \(6 \times 4 = 24\) hundredths, which is \(0.24\).
Places in the question \(=\) places in the answer:
| Question | Digits, places | Answer |
|---|---|---|
| \(0.32 \times 0.02\) | \(64\), \(2 + 2 = 4\) | \(0.0064\) |
| \(1.1 \times 0.05\) | \(55\), \(1 + 2 = 3\) | \(0.055\) |
| \(1.23 \times 0.2\) | \(246\), \(2 + 1 = 3\) | \(0.246\) |
Multiplying by a number between \(0\) and \(1\) makes a positive number smaller:
How to multiply decimals
- Estimate the answer.
- Multiply the numbers as if there were no decimal points.
- Count the decimal places in both numbers and add them.
- Place the point that many places from the right, writing zeros in front if needed. Check with the estimate.
(i) \(0.32 \times 0.02\)
(ii) \(1.1 \times 0.05\)
(i) \(32 \times 2 = 64\); places \(2 + 2 = 4\).
(ii) \(11 \times 5 = 55\); places \(1 + 2 = 3\).
| \(0.32 \times 0.02\) | \(=\) | \(0.0064\) |
| \(1.1 \times 0.05\) | \(=\) | \(0.055\) |
(i) \(0.0064\)
(ii) \(0.055\)
(i) \(0.6 \times 7\)
(ii) \(2.35 \times 4\)
| \(0.6 \times 7\) | \(=\) | \(4.2\) |
| \(2.35 \times 4\) | \(=\) | \(9.40 = 9.4\) |
(i) \(6\) tenths \(\times 7 = 42\) tenths \(= 4.2\)
(ii) \(235 \times 4 = 940\), \(2\) places: \(9.40 = 9.4\)
(i) \(1.6 \times 0.3\)
(ii) \(0.8 \times 0.07\)
| \(1.6 \times 0.3\) | \(=\) | \(48 \div 100 = 0.48\) |
| \(0.8 \times 0.07\) | \(=\) | \(56 \div 1000 = 0.056\) |
(ii) needs \(3\) places, so write a zero in front of \(56\).
| \(6 \times 145\) | \(=\) | \(870\) |
| \(0.6 \times 14.5\) | \(=\) | \(870 \div 100 = 8.7\) |
Estimate \(0.6 \times 15 = 9\). The cheese costs \(\$8.70\).
| \(645 \times 38\) | \(=\) | \(645 \times 30 + 645 \times 8\) |
| \(\) | \(=\) | \(19\,350 + 5160\) |
| \(\) | \(=\) | \(24\,510\) |
Places \(1 + 2 = 3\), so \(3.8 \times 6.45 = 24.510\). Estimate \(4 \times 6.5 = 26\). It costs \(\$24.51\).
| \(15 \times 6\) | \(=\) | \(90\) |
| \(1.5 \times 0.6\) | \(=\) | \(90 \div 100 = 0.9\) |
The area is \(0.9\) m\(^2\). Count the places before dropping the end zero.
Common pitfalls
Frequently asked questions
How do you multiply two decimals?
Multiply without the points, then count the decimal places in both numbers. \(1.6 \times 0.3 = 0.48\).
Why do tenths times tenths give hundredths?
On a grid, \(0.6\) by \(0.4\) covers \(24\) of the \(100\) small squares, so it is \(0.24\).
What if there are not enough digits for the point?
Write zeros in front. \(0.8 \times 0.07 = 0.056\).
Does multiplying by 0.5 make a number bigger?
No. It halves it. \(20 \times 0.5 = 10\).
How do you check a decimal product?
Estimate by rounding. \(4.8 \times 2.1 \approx 10\), so \(10.08\) makes sense.