GCSE Maths Practice: decimals

Question 2 of 10

This question tests your understanding of multiplying two decimals. It helps you practise counting decimal places and placing the decimal point correctly in your answer.

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\( \begin{array}{l}\textbf{Calculate } 0.4 \times 0.3.\end{array} \)

Choose one option:

Count the total number of decimal places in both numbers before placing the decimal point in your answer. Always estimate first to check if your result makes sense.

Multiplying Two Decimals

When you multiply two decimals, the steps are similar to multiplying whole numbers, except you must account for the total number of decimal places. The key idea is that each decimal place divides the number by ten, so multiplying two decimals makes the product smaller than either number alone.

Step-by-Step Method

  1. Ignore the decimals temporarily and multiply as if they were whole numbers.
  2. Count the total number of digits after the decimal in both numbers.
  3. In your answer, move the decimal point to the left by that total number of places.
  4. Check that your result is smaller than both original numbers—if not, recheck your decimal placement.

Worked Examples

Example 1: 0.2 × 0.5 = ?
2 × 5 = 10 → two decimal places → 0.10.

Example 2: 0.6 × 0.4 = ?
6 × 4 = 24 → two decimal places → 0.24.

Example 3: 0.35 × 0.2 = ?
35 × 2 = 70 → three decimal places → 0.070.

Example 4: 1.5 × 0.3 = ?
15 × 3 = 45 → two decimal places → 0.45.

Common Mistakes

  • Forgetting to count both decimals: Always count the decimal places in both numbers combined.
  • Placing the decimal incorrectly: Moving it one place instead of two changes the answer by a factor of 10.
  • Expecting the answer to be larger: Multiplying decimals smaller than 1 always gives a smaller result.

Real-Life Applications

Multiplying decimals is essential in financial, scientific, and measurement problems. For example:
• £0.40 × 0.3 = £0.12 — calculating a 30% discount on 40p.
• 0.4 m × 0.3 m = 0.12 m² — finding the area of a small rectangle.
• 0.8 × 0.25 = 0.20 — determining a fractional portion of a quantity.

These everyday contexts reinforce why accuracy with decimal places is so important.

FAQs

1. Why is the answer smaller when multiplying decimals?
Each decimal factor represents a portion of a whole, so multiplying them gives a smaller piece of that whole.

2. How can I check my work?
Estimate first: 0.4 is about ½, and 0.3 is about ⅓, so the answer should be roughly 0.1–0.2. That matches 0.12.

3. What if one number is a whole number?
Use the same rule—just count decimal places in the decimal number and adjust your answer accordingly.

4. Do I need to add zeros after the answer?
Only if the context (like money) requires it, e.g., £0.10 instead of 0.1.

Study Tip

Practise multiplying decimals by sketching a grid or using a calculator to check patterns. For instance, 0.1 × 0.1 = 0.01, 0.2 × 0.3 = 0.06, and 0.5 × 0.5 = 0.25. You’ll quickly recognise that two decimals less than one always give an even smaller product.

Mastering decimal multiplication lays the foundation for work with percentages, proportions, and real-world problem solving in GCSE Maths.