Multiplying Decimals – Count the Places
Multiplying decimals does not require you to line up decimal points. Instead, you ignore the decimal points temporarily, multiply as if you are working with whole numbers, and then place the decimal point back in the answer by counting decimal places.
The Decimal-Place Rule
Count the total number of decimal places in both numbers being multiplied. That is how many decimal places the answer must have.
Simple Examples
4 times 3 = 12. Decimal places: 1+1=2. Place point 2 digits from right: 0.12. Answer: 0.12.
25 times 3 = 75. One decimal place total. Answer: 7.5.
14 times 23 = 322. Two decimal places. Answer: 3.22.
Two Decimal Places
456 times 7 = 3192. Three decimal places total (2+1). Answer: 3.192.
235 times 14 = 3290. Three decimal places. Answer: 3.290 = 3.29.
Multiplying by Powers of 10
| Calculation | Shortcut | Answer |
|---|---|---|
| 3.72 times 10 | Shift point 1 right | 37.2 |
| 3.72 times 100 | Shift point 2 right | 372 |
| 3.72 times 1000 | Shift point 3 right | 3720 |
Estimating First
Always estimate before multiplying: 4.8 times 3.1 is roughly 5 times 3 = 15. When you calculate 4.8 times 3.1 = 14.88, your estimate confirms this is reasonable.
Real-Life Example
Petrol costs £1.72 per litre. You buy 12.5 litres. Cost = 1.72 times 12.5. 172 times 125 = 21500. Three decimal places. £21.500 = £21.50.
Key Takeaways
- Ignore decimal points during multiplication; multiply the digits.
- Count total decimal places in both factors to place the point in the answer.
- Multiplying by 10 shifts the decimal point right.
- Always estimate first to check your answer is sensible.
Practice Questions
- 0.6 times 0.5
- 3.7 times 4
- 2.45 times 0.8
- 1.6 times 2.5
- A carpet is 4.2 m wide and 3.75 m long. What is its area?