Year 6 Arithmetic (SATs): Multiplying decimals by whole numbers
Part of the Year 6 Arithmetic (SATs) decimals and percentages chapter. Chapter overview · whole chapter on one page
Multiplying decimals by whole numbers
Rule
Multiply as if there were no decimal point, then put the point back so the answer has the same number of decimal places as the decimal.
For a two-digit whole number, use two partial products: multiply by the ones digit, then by the tens digit, then add.
Key ideas
- Ignore the decimal point, multiply, then put it back.
- The answer has the same number of decimal places as the decimal number.
- Estimate first to check the size of the answer.
Method. Use two partial products, then put the decimal point back.
- Multiply by the ones digit. Multiply the digits 125 by 4.125 × 4 = 500
- Multiply by the tens digit. Multiply the digits 125 by 10, which is 1 tens.125 × 10 = 1250
- Add the two parts. Add the partial products.500 + 1250 = 1750
- Put the decimal point back. 1.25 has 2 decimal places, so the answer has 2.1750 → 17.50
- Write the answer. 17.50
Check. About 1 × 14 = 14, and 17.5 is about right. ✓
Watch out. Keep the two decimal places in the answer: 17.50.
Method. Multiply 37 by 6, then put the point back.
- Ignore the decimal point for now. Multiply the digits 37 by 6, as whole numbers.37 × 6 = 222
- Put the decimal point back. 3.7 has 1 decimal place, so the answer has 1.222 → 22.2
- Write the answer. 22.2
Check. About 4 × 6 = 24, close to 22.2. ✓
Method. Multiply 46 by 8, then put the point back.
- Ignore the decimal point for now. Multiply the digits 46 by 8, as whole numbers.46 × 8 = 368
- Put the decimal point back. 0.46 has 2 decimal places, so the answer has 2.368 → 3.68
- Write the answer. 3.68
Check. 0.5 × 8 = 4, close to 3.68. ✓
Exercise 4C Practice: multiplying decimals by whole numbers
Non-calculatorMethod. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 34 by 5, as whole numbers.34 × 5 = 170
- Put the decimal point back. 3.4 has 1 decimal place, so the answer has 1.170 → 17.0
- Write the answer. 17.0
Check. About 3 × 5 is close to 17.0. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 236 by 4, as whole numbers.236 × 4 = 944
- Put the decimal point back. 2.36 has 2 decimal places, so the answer has 2.944 → 9.44
- Write the answer. 9.44
Check. About 2 × 4 is close to 9.44. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 185 by 6, as whole numbers.185 × 6 = 1110
- Put the decimal point back. 1.85 has 2 decimal places, so the answer has 2.1110 → 11.10
- Write the answer. 11.10
Check. About 2 × 6 is close to 11.10. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 46 by 8, as whole numbers.46 × 8 = 368
- Put the decimal point back. 0.46 has 2 decimal places, so the answer has 2.368 → 3.68
- Write the answer. 3.68
Check. About 0 × 8 is close to 3.68. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Multiply by the ones digit. Multiply the digits 625 by 2.625 × 2 = 1250
- Multiply by the tens digit. Multiply the digits 625 by 10, which is 1 tens.625 × 10 = 6250
- Add the two parts. Add the partial products.1250 + 6250 = 7500
- Put the decimal point back. 6.25 has 2 decimal places, so the answer has 2.7500 → 75.00
- Write the answer. 75.00
Check. About 6 × 12 is close to 75.00. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Multiply by the ones digit. Multiply the digits 407 by 3.407 × 3 = 1221
- Multiply by the tens digit. Multiply the digits 407 by 20, which is 2 tens.407 × 20 = 8140
- Add the two parts. Add the partial products.1221 + 8140 = 9361
- Put the decimal point back. 4.07 has 2 decimal places, so the answer has 2.9361 → 93.61
- Write the answer. 93.61
Check. About 4 × 23 is close to 93.61. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Multiply by the ones digit. Multiply the digits 85 by 4.85 × 4 = 340
- Multiply by the tens digit. Multiply the digits 85 by 10, which is 1 tens.85 × 10 = 850
- Add the two parts. Add the partial products.340 + 850 = 1190
- Put the decimal point back. 0.85 has 2 decimal places, so the answer has 2.1190 → 11.90
- Write the answer. 11.90
Check. About 1 × 14 is close to 11.90. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 76 by 9, as whole numbers.76 × 9 = 684
- Put the decimal point back. 7.6 has 1 decimal place, so the answer has 1.684 → 68.4
- Write the answer. 68.4
Check. About 8 × 9 is close to 68.4. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Ignore the decimal point for now. Multiply the digits 125 by 4, as whole numbers.125 × 4 = 500
- Put the decimal point back. 12.5 has 1 decimal place, so the answer has 1.500 → 50.0
- Write the answer. 50.0
Check. About 12 × 4 is close to 50.0. ✓
Method. Multiply as whole numbers, then put the decimal point back.
- Multiply by the ones digit. Multiply the digits 39 by 6.39 × 6 = 234
- Multiply by the tens digit. Multiply the digits 39 by 10, which is 1 tens.39 × 10 = 390
- Add the two parts. Add the partial products.234 + 390 = 624
- Put the decimal point back. 0.39 has 2 decimal places, so the answer has 2.624 → 6.24
- Write the answer. 6.24
Check. About 0 × 16 is close to 6.24. ✓
Method. Multiply the price by the number of pens.
- Multiply by the ones digit. Multiply the digits 125 by 4.125 × 4 = 500
- Multiply by the tens digit. Multiply the digits 125 by 10, which is 1 tens.125 × 10 = 1250
- Add the two parts. Add the partial products.500 + 1250 = 1750
- Put the decimal point back. 1.25 has 2 decimal places, so the answer has 2.1750 → 17.50
- Write the answer. £17.50
Check. 14 pens at £1 each is £14, and £17.50 is a little more. ✓
Method. Multiply the weight of one packet by 12.
- Multiply by the ones digit. Multiply the digits 75 by 2.75 × 2 = 150
- Multiply by the tens digit. Multiply the digits 75 by 10, which is 1 tens.75 × 10 = 750
- Add the two parts. Add the partial products.150 + 750 = 900
- Put the decimal point back. 0.75 has 2 decimal places, so the answer has 2.900 → 9.00
- Write the answer. 9.00 kg
Check. 12 × 0.75 = 9. ✓
Method. Round both numbers, multiply them, then compare with the exact answer.
- Round. 6.8 → 7 and 19 → 20.7 × 20
- Estimate. 7 × 20 = 140.140
- Compare. The exact answer is 6.8 × 19 = 129.2, which is close to 140.129.2
- Write the answer. The estimate is 140, and 129.2 is close to it because 7 × 20 = 140 is near 6.8 × 19 = 129.2.
Check. The estimate is a little more than the exact answer. ✓
Method. Use the whole-number method, then put the point back.
- Ignore the decimal point for now. Multiply the digits 405 by 3, as whole numbers.405 × 3 = 1215
- Put the decimal point back. 4.05 has 2 decimal places, so the answer has 2.1215 → 12.15
- Write the answer. 12.15
Check. 4.05 is about 4, and 4 × 3 = 12, close to 12.15. ✓