Practice Maths

L29 — Multiplying, Dividing and Rounding Decimals

Key Terms

decimal places
The number of digits after the decimal point. E.g., 3.47 has 2 decimal places.
significant figures
Digits counted from the first non-zero digit. E.g., 0.0047 has 2 significant figures (4 and 7).
rounding
Replacing a number with a nearby approximation. Look at the digit after the rounding position: if it is 5 or more, round up; if 4 or less, round down.
divisor
The number you divide by. E.g., in 4.8 ÷ 0.6, the divisor is 0.6.

Key Methods

Multiplying decimals: Multiply ignoring the decimal point, then count the total decimal places in both factors and place the decimal point that many places from the right.

Dividing by a decimal: Multiply both numbers by the same power of 10 to make the divisor a whole number, then divide.

Rounding to decimal places: Look at the digit one position to the right of the rounding position. If 5 or more, round up; if 4 or less, round down.

Worked Example

Calculate 2.4 × 1.5

Step 1 — Count decimal places: 2.4 has 1, 1.5 has 1 → 2 total

Step 2 — Multiply ignoring decimals: 24 × 15 = 360

Step 3 — Place decimal (2 places from right): 360 → 3.60 = 3.6

Multiplying Decimals

The trick to multiplying decimals is to ignore the decimal points, multiply the whole numbers, then place the decimal back in. The number of decimal places in your answer equals the total number of decimal places in the two numbers you multiplied.

  • 0.3 × 0.4: ignore decimals → 3 × 4 = 12. Total decimal places = 1 + 1 = 2. Answer: 0.12
  • 1.2 × 3: ignore decimal → 12 × 3 = 36. Decimal places = 1. Answer: 3.6
  • 2.5 × 1.4: 25 × 14 = 350. Decimal places = 1 + 1 = 2. Answer: 3.50 = 3.5

Dividing Decimals

To divide decimals, make the divisor (the number you’re dividing by) a whole number. Multiply both numbers by the same power of 10:

  • 2.4 ÷ 0.6: multiply both by 10 → 24 ÷ 6 = 4
  • 3.6 ÷ 0.04: multiply both by 100 → 360 ÷ 4 = 90
  • 5.0 ÷ 0.25: multiply both by 100 → 500 ÷ 25 = 20

Rounding to Decimal Places

To round to a given number of decimal places, look at the digit one position to the right of where you want to round:

  • If that digit is 5 or more: round up (increase the last kept digit by 1).
  • If that digit is 4 or less: round down (leave the last kept digit unchanged).

Example: round 3.4762 to 2 decimal places. Look at the third decimal place: 6. Since 6 ≥ 5, round up. Answer: 3.48

Rounding to Significant Figures

Significant figures count from the first non-zero digit. Round 0.004738 to 2 significant figures:

  • The leading zeros are not significant. The first sig fig is 4, the second is 7.
  • Look at the third sig fig (3): since 3 < 5, round down. Answer: 0.0047
A common mistake in multiplying decimals is losing track of decimal places. Count the decimal digits in each factor BEFORE you start. For example, 0.12 × 0.5 has 2 + 1 = 3 decimal places, so 12 × 5 = 60 becomes 0.060 = 0.06. Always count first!

  1. Multiply by a whole number

    1. 6.4 × 2
    2. 5.6 × 3
    3. 4.3 × 3
    4. 7.8 × 4
    5. 3.5 × 5
    6. 9.2 × 6

  2. Divide by a whole number

    1. 6.3 ÷ 3
    2. 9.6 ÷ 3
    3. 6.2 ÷ 2
    4. 8.4 ÷ 4
    5. 7.5 ÷ 5
    6. 18.6 ÷ 6

  3. Round to 1 decimal place

    1. 3.47
    2. 8.62
    3. 1.95
    4. 7.03
    5. 5.78

  4. Multiply a decimal by a decimal

    1. 1.2 × 1.5
    2. 2.4 × 2.5
    3. 3.6 × 1.2
    4. 0.8 × 0.6
    5. 4.5 × 2.2
    6. 1.25 × 0.4

  5. Divide a decimal by a decimal

    1. 4.8 ÷ 0.6
    2. 2.8 ÷ 0.4
    3. 2.1 ÷ 0.3
    4. 3.6 ÷ 0.9
    5. 6.0 ÷ 1.2
    6. 5.5 ÷ 0.5

  6. Petrol Problem

    Petrol costs $1.85 per litre. How much does 8 litres cost?

  7. Ribbon Cutting

    A piece of ribbon is 4.5 m long. It is cut into 6 equal pieces. How long is each piece?

  8. Round to 2 decimal places

    1. 3.475
    2. 12.664
    3. 0.985
    4. 7.316
    5. 1.005

  9. Pizza Sharing

    4 friends share the cost of a pizza equally. The total cost is $23.60. How much does each person pay?

  10. Speed Problem

    A car travels at 62.5 km/h for 2.4 hours. How far does it travel? Round to 1 decimal place.

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