Multiplying decimals worksheet

Part A: Working out and filling in

1. 1. 6.92 × 1000 = 6920

   6.92 × 1000: ×1000 moves the point three places right, filling in zeros at the end, 6.92 × 1000 = 6920

2. 2. 8.28 × 10 = 82.8

   8.28 × 10: ×10 moves the point one place right, 8.28 × 10 = 82.8

3. 3. 0.667 × 1000 = 667

   0.667 × 1000: ×1000 moves the point three places right, and the zeros left at the front aren't written, 0.667 × 1000 = 667

4. 4. 1500

   10² is two 10s multiplied. Work out what 10² is, then multiply 15 by it.

   10² = 100: 15 × 100 = 1500, two 0s on the end.

5. 5. 3800

   10³ is three 10s multiplied. When you multiply 3.8 by it, how many places right does the point move?

   10³ = 1000: the point moves three places right, with 0s to fill: 3.8 × 1000 = 3800.

6. 6. 96.276

   × 0.1 is the same as ÷ 10. Which way does the point in 962.76 move, and by how many places?

   × 0.1 is ÷ 10: the point moves one place left, 96.276.

7. 7. 0.7 × 4 = 2.8

   0.7 × 4: multiply as whole numbers, 7 × 4 = 28; 0.7 has one place, so put the point back one place into 28 → 2.8

8. 8. 0.5 × 0.9 = 0.45

   0.5 × 0.9: multiply as whole numbers, 5 × 9 = 45; 0.5 has one place and 0.9 has one place, 1 + 1 = 2 in all, so put the point back two places into 45 → 0.45

9. 9. 44.85

   For two decimal places, the thousandths digit decides. Find it in 44.8489 first.

   The thousandths digit, 8, decides the hundredths: 44.8489 ≈ 44.85.

10. 10. 37.7

    To round to one decimal place, the hundredths digit decides. Find the hundredths digit of 37.708 first.

    Look at the hundredths, 0: 0–4 down, 5–9 up. 37.708 ≈ 37.7.

Part B: Choose, or true or false

1. 11. B. 10²

   The small number on the 10 says how many 10s are multiplied. How many 10s multiply to make 100?

   Count the 0s after the 1 in 100: that is the small number on the 10.

2. 12. True

   No working needed: is 100 more or less than 1?

   Multiplying by more than 1 makes it bigger; by less than 1 (0.1, 0.01, 0.001), smaller.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. Highlighters cost $6.5 each. An office buys 100 of them. How many dollars must it pay? (Answer: 650 dollars)

   6.5 × 100 = 650

2. 14. A coin weighs 4.5 g. How many grams do 100 such coins weigh? (Answer: 450 g)

   4.5 × 100 = 450

3. 15. 830 cm

   Metres to centimetres is × 10², which is 100. How many places right does the point in 8.3 move?

   8.3 × 10² = 8.3 × 100 = 830: the point moves two places right.

4. 16. 83.6 mm

   836 sheets is 836 × 0.1 mm. Multiplying by 0.1 is the same as dividing by what?

   836 × 0.1 = 836 ÷ 10 = 83.6 mm.

5. 17. Cloth costs $4.7 a metre. Mum buys 2.4 m of it. How many dollars must she pay? (Answer: 11.28 dollars)

   4.7 × 2.4 = 11.28

6. 18. 5 kg

   Weight = weight a metre × length: work out 2.81 × 1.78 exactly, and look at the thousandths only at the end.

   2.81 × 1.78 = 5.0018 ≈ 5 kg: the exact product first, rounded only at the end.