Practice Maths

L37 — Multiplying Decimals in Context

Key Terms

decimal places
The digits after the decimal point. E.g. 3.47 has 2 decimal places. When multiplying, add the decimal places in both factors to find how many places the answer needs.
estimate
A rough calculation used to check whether an answer is reasonable. Round each number before multiplying to get a quick mental result.
decimal multiplier
A decimal used to apply a percentage increase or decrease. E.g. multiplying by 1.1 adds 10%; multiplying by 0.8 removes 20%.
GST (Goods and Services Tax)
A 10% tax added to most goods and services in Australia. To find the GST-inclusive price, multiply by 1.1.

Multiplying Decimals

  1. Estimate first — round each number to check your answer is reasonable.
  2. Count decimal places — add together the number of decimal places in both factors.
  3. Multiply ignoring the decimal point — treat both numbers as whole numbers.
  4. Place the decimal point — count in from the right the total number of decimal places.

Multiplying and Dividing by Powers of 10

  • × 10 → shift decimal 1 place right
  • × 100 → shift decimal 2 places right
  • × 1000 → shift decimal 3 places right
  • ÷ 10 → shift decimal 1 place left
  • ÷ 100 → shift decimal 2 places left
  • ÷ 1000 → shift decimal 3 places left
Always estimate first! Before multiplying, round each number and do a quick mental check. If 3.4 × 2.5, estimate 3 × 3 = 9, so the answer should be around 8–9. If your answer is way off, recheck your decimal placement.

Worked Examples

3.4 × 2.5
Estimate: 3 × 3 = 9
Decimal places: 1 + 1 = 2 d.p.
34 × 25 = 850
Place decimal: 8.50 → 8.5

0.06 × 0.3
Estimate: 0.06 × 0.3 ≈ 0 (very small)
Decimal places: 2 + 1 = 3 d.p.
6 × 3 = 18
Place decimal: 0.018 → 0.018

15.6 ÷ 4
Estimate: 16 ÷ 4 = 4
156 ÷ 4 = 39
Place decimal (1 d.p.): 3.9

Why Decimal Multiplication Feels Different

Multiplying decimals feels tricky because unlike whole numbers, the result can be smaller than what you started with. 0.5 × 0.5 = 0.25 — smaller than both factors! This makes sense because 0.5 × 0.5 means “half of a half,” which is a quarter. Students often expect multiplication to always make things bigger. With decimals, it doesn’t have to.

The Count-and-Place Method

Here is the reliable method for multiplying any two decimals:

  1. Estimate: round both numbers and multiply mentally. This is your sanity check.
  2. Count decimal places: add up the total number of decimal places in both numbers.
  3. Multiply the digits as if they were whole numbers (ignore decimal points).
  4. Place the decimal point by counting in that many places from the right.

Example: 3.4 × 2.5. Estimate: 3 × 3 = 9. Decimal places: 1 + 1 = 2. Whole number multiplication: 34 × 25 = 850. Place decimal 2 places from right: 8.50 = 8.5. Reasonable? Yes, close to 9. Done!

Remember: Count and total the decimal places in BOTH factors, then place the decimal in the answer that many places from the right. Never count the places in the answer — always count them in the factors and then place.

Multiplying by Powers of 10: The Decimal Point Shift

Multiplying by a power of 10 shifts the decimal right; dividing shifts it left. The number of places equals the number of zeros in the power of 10. This is the fastest calculation method for these problems:

  • 3.74 × 10 = 37.4 (shift 1 right)
  • 3.74 × 100 = 374 (shift 2 right)
  • 84.5 ÷ 10 = 8.45 (shift 1 left)

Real-Life Decimal Multiplication: Shopping and GST

Australian prices often include GST (Goods and Services Tax) at 10%. To add GST, multiply by 1.1. To remove GST, divide by 1.1. A discount of 20% means you pay 80%, so multiply by 0.8. These decimal multipliers are used millions of times every day in Australian retail, accounting, and budgeting.

For example: a jacket costs $85. With 10% GST: 85 × 1.1 = $93.50. With a 20% discount instead: 85 × 0.8 = $68. Understanding which multiplier to use is a genuine life skill.

Common Mistake: Forgetting to count decimal places from BOTH factors. Students sometimes count only the places in the larger number. In 0.06 × 0.3, there are 2 + 1 = 3 decimal places total. 6 × 3 = 18, so the answer is 0.018 — not 0.18 or 1.8!

  1. Multiply Decimals — Fluency

    Calculate each product. Show your decimal place count.

    1. 3.2 × 4
    2. 0.7 × 5
    3. 1.5 × 1.2
    4. 0.4 × 0.8
    5. 2.3 × 3
    6. 5.6 × 0.2
    7. 0.09 × 0.7
    8. 4.5 × 2.4

  2. Divide Decimals — Fluency

    Calculate each quotient.

    1. 8.4 ÷ 4
    2. 6.3 ÷ 7
    3. 15 ÷ 0.5
    4. 2.4 ÷ 0.8
    5. 0.36 ÷ 0.9
    6. 12.6 ÷ 3
    7. 4.5 ÷ 0.15
    8. 0.48 ÷ 0.06

  3. Powers of 10

    Multiply or divide by shifting the decimal point:

    1. 3.74 × 10
    2. 0.56 × 100
    3. 2.1 × 1000
    4. 84.5 ÷ 10
    5. 630 ÷ 100
    6. 4500 ÷ 1000
    7. 0.08 × 100
    8. 0.007 × 1000

  4. Estimate and Evaluate

    1. Estimate 4.8 × 3.1 by rounding, then calculate the exact answer.
    2. Estimate 9.7 × 2.9 by rounding, then calculate the exact answer.
    3. A student wrote 2.3 × 0.4 = 9.2. Identify the error and give the correct answer.
    4. A student wrote 0.5 × 0.5 = 2.5. Identify the error and give the correct answer.
    5. True or False: 0.3 × 0.3 = 0.9. Explain your reasoning.
    6. Without calculating, decide which is larger: 3.6 × 0.9 or 3.6 × 1.1. Explain.

  5. Shopping and Costs

    1. Apples cost $4.20 per kg. How much would 3.5 kg cost?
    2. A book costs $12.95. How much do 4 books cost?
    3. Petrol costs $2.15 per litre. How much does 40.5 litres cost?
    4. A ribbon costs $3.60 per metre. How much does 2.5 metres cost?
    5. Three items cost $8.50, $4.75, and $12.30. What is the total cost?
    6. You pay $50 for items totalling $37.85. How much change do you receive?

  6. GST, Discounts and Scaling

    1. A jacket costs $85. GST adds 10% to the price. Calculate the total price including GST by multiplying by 1.1.
    2. A laptop is priced at $1240 before GST. What is the GST-inclusive price?
    3. A shirt costs $60 and is on sale with a 20% discount. Multiply by 0.8 to find the sale price.
    4. A restaurant offers a 15% discount to students. A meal costs $24.00. What do students pay?
    5. A recipe for 4 people uses 0.75 kg of flour. How much flour is needed for 10 people?
    6. Paint covers 12.5 m² per litre. How many litres are needed to cover 43.75 m²?

  7. Distance, Rate and Fuel

    1. A car travels at 65.5 km/h for 3 hours. How far does it travel?
    2. A cyclist rides 2.4 km every 10 minutes. How far do they ride in 1.5 hours (90 minutes)?
    3. A car uses 8.5 litres of fuel per 100 km. How much fuel is needed for a 250 km trip?
    4. Fuel costs $2.08 per litre. Using your answer from part (c), what is the total fuel cost?
    5. A train travels 312.5 km in 2.5 hours. What is its average speed in km/h?
    6. A leaking tap drips 0.25 litres per hour. How much water is wasted in 2.5 days?

  8. Mixed Operations Review

    Choose the correct operation and calculate:

    1. A bottle of juice holds 1.25 litres. How many millilitres is that?
    2. Three friends split the cost of a $28.50 meal equally. How much does each pay?
    3. A car travels 0.25 km every minute. How far does it travel in 24 minutes?
    4. A box of 6 chocolate bars costs $7.20. What does each bar cost?
    5. A snail moves at 0.045 km per hour. How far does it travel in 4 hours?
    6. Three pieces of ribbon measure 1.2 m, 0.85 m and 2.4 m. What is the total length?

  9. Measurement and Area

    1. A rectangular garden is 6.4 m long and 3.5 m wide. What is its area?
    2. Carpet costs $24.50 per square metre. What is the cost of carpeting a room that is 4.2 m by 3.8 m?
    3. A floor tile is 0.45 m by 0.45 m. How many tiles are needed to cover a floor that is 4.5 m by 3.6 m?
    4. A farmer’s paddock is 2.4 km long and 1.75 km wide. What is its area in square kilometres?

  10. Budgeting and Financial Maths

    1. Maya earns $14.50 per hour. She works 6.5 hours on Saturday and 4.75 hours on Sunday. How much does she earn in total for the weekend?
    2. A mobile phone plan costs $39.95 per month. How much does it cost per year?
    3. Ben earns $18.40 per hour. After saving 0.3 of his weekly pay, he spends the rest. If he earns $110.40 in a week, how much does he spend?
    4. A supermarket sells 1.5 kg bags of rice for $3.75 and 2.5 kg bags for $5.50. Which is the better value per kilogram? Justify your answer.
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