Multiplication and division (2)
Multiplying decimals
Here you learn to estimate and then multiply a number with up to 2 decimal places by a 1-digit or a 2-digit whole number. Always start with an estimate so you can check your answer is sensible.
Always estimate first
Before you calculate, round both numbers to make a rough answer. This tells you how big the real answer should be and helps you place the decimal point. Example: for 45.75 × 63, round to 50 × 60 = 3000, so the answer should be near 3000.
Multiplying by a 1-digit number
Multiply as if there were no decimal point, keeping the place value of each digit. The answer has the same number of decimal places as the number you started with. Example: 40.09 × 9. 40 × 9 = 360 and 0.09 × 9 = 0.81, so 40.09 × 9 = 360.81.
Multiplying by a 2-digit number
Split the 2-digit number into tens and ones. Multiply the decimal by the ones, then by the tens, and add the two results together. These stages can be done in either order. Example: 45.75 × 63 = (45.75 × 3) + (45.75 × 60) = 137.25 + 2745 = 2882.25.
Placing the decimal point and checking
Once you have the digits, use your estimate to place the decimal point. Then check the answer is close to the estimate. For 45.75 × 63 the estimate was 3000 and the answer 2882.25 is close, so it is sensible.
Worked examples
Estimate before multiplying
- You want 45.75 × 63.
- Round 45.75 to 50 and 63 to 60.
- Multiply the rounded numbers: 50 × 60.
Answer: Estimate: 50 × 60 = 3000, so the answer should be near 3000.
Multiply a decimal by a 1-digit number
- Calculate 40.09 × 9.
- Multiply the whole part: 40 × 9 = 360.
- Multiply the decimal part: 0.09 × 9 = 0.81.
- Add the parts together.
Answer: 40.09 × 9 = 360.81
Multiply a decimal by a 2-digit number
- Calculate 45.75 × 63.
- Multiply by the ones: 45.75 × 3 = 137.25.
- Multiply by the tens: 45.75 × 60 = 2745.
- Add the two answers together and check against the estimate of 3000.
Answer: 45.75 × 63 = 137.25 + 2745 = 2882.25
A money problem
- Meals cost $15.25 each and 12 people go for a meal.
- Estimate first: 15 × 12 = 180.
- Multiply by the ones and tens: 15.25 × 2 = 30.5 and 15.25 × 10 = 152.5.
- Add them together.
Answer: 15.25 × 12 = 152.5 + 30.5 = $183
Where you see this in real life
- Working out the total cost of many theatre tickets that each cost $45.75.
- Finding the total bill when several meals cost the same amount.
- Working out how much a call costs at a fixed price for each minute.
- Buying several packs of stickers at the same price.
Key words
- Decimal number
- A number with digits after a decimal point, such as 45.75.
- Decimal point
- The dot that separates the whole part from the fraction part of a number.
- Decimal place
- A position after the decimal point — tenths, hundredths, and so on.
- Product
- The result of multiplying numbers together.
- Estimate
- A rough answer found by rounding, used to check the real answer.