GCSE Maths Practice: decimals

Question 1 of 10

This GCSE Higher-level problem extends decimal multiplication into applied scientific and measurement contexts, building precision and reasoning beyond simple arithmetic.

›

\( \begin{array}{1}\textbf{A chemist measures a liquid with density } 0.12\,\text{g/cm}^3 \text{ and volume } 0.04\,\text{cm}^3.\\\text{ Calculate the mass of the sample in grams.}\end{array} \)

Choose one option:

Estimate first: 0.1 × 0.04 ≈ 0.004. If your answer is close, the decimal point is probably in the right place.

At GCSE Higher level, decimal multiplication often appears in applied situations such as area, density, or probability calculations. This question deepens understanding of place value and accuracy when both numbers are less than one.

Scenario Context

A chemist needs to calculate the mass of a solution sample. The density is 0.12 g/cm³ and the volume is 0.04 cm³. The mass equals density × volume:

\(\text{mass} = 0.12 \times 0.04 = 0.0048\,\text{g}.\)

This is a realistic context where small decimal values represent very small quantities, requiring careful handling of decimal places.

Step-by-Step Method

  1. Ignore the decimals. Treat 0.12 and 0.04 as 12 and 4 for now: 12 × 4 = 48.
  2. Count decimal places. The first factor (0.12) has 2 decimal places, and the second (0.04) has 2. Together, that makes 4 decimal places.
  3. Place the decimal point. Move it 4 places left in 48 → 0.0048.
  4. Interpret the answer. The product represents 0.0048 g — less than one gram, which makes sense.

Common Mistakes

  • Moving the decimal point the wrong number of places.
  • Multiplying directly on a calculator without estimating first, leading to misplaced zeros.
  • Writing 0.048 or 0.00048 — both ten times too large or too small.
  • Forgetting to interpret the units in context (grams, cm², etc.).

Advanced Understanding

In science or engineering questions, you may be asked to express results in standard form. Here, 0.0048 = 4.8 × 10⁻³ g. Recognising equivalence between decimal and scientific notation is a key Higher skill that links number work with physics and chemistry applications.

Worked Example 1

Find the area of a rectangle measuring 0.12 m by 0.04 m.

\(\text{Area} = 0.12 \times 0.04 = 0.0048\,\text{m}^2.\)

Convert to cm²: 0.0048 × 10,000 = 48 cm².

Worked Example 2

Calculate the probability of two independent events. If P(A) = 0.12 and P(B) = 0.04, then P(A and B) = 0.12 × 0.04 = 0.0048 (0.48%).

FAQ

Q1: How do I know how many zeros to include?
A1: Count the total number of decimal places across both numbers. Each decimal place shifts the point one position to the left in the product.

Q2: Why estimate before multiplying?
A2: Estimation (≈ 0.1 × 0.04 = 0.004) checks that your final digits are realistic and helps spot misplaced decimals.

Q3: Can I rely on the calculator?
A3: Use it to verify, but always confirm place value mentally. Examiners often expect written justification of decimal placement.

Study Tip

Think in powers of ten: multiplying 0.12 × 0.04 is equivalent to (12 × 4) ÷ 10⁴. This mental model ensures accuracy when decimals become smaller.

Mastering decimal multiplication at this precision prepares you for topics such as density, pressure, compound measures, and probability in the Higher GCSE Maths paper.