GCSE Maths Practice: decimals

Question 2 of 10

This GCSE Higher-level question combines decimal addition with unit conversion. It mirrors real measurement problems found in physics, engineering, and design tasks.

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\( \begin{array}{1}\textbf{A metal rod is made of three sections measuring 0.12 m, 0.375m, and 0.375m.}\\ \text{Calculate the total length in metres.}\end{array} \)

Choose one option:

Estimate before calculating exactly — 0.1 + 0.4 + 0.4 ≈ 0.9 m — to ensure your final answer is reasonable.

This Higher-tier GCSE Maths question tests your ability to handle decimals in a measurement context. The task simulates the kind of reasoning used in science or engineering problems, where you must combine decimal values representing different physical quantities before interpreting or converting them.

Scenario Context

A surveyor measures three short sections of a metal rod using a precision caliper. The lengths are 0.125 m, 0.375 m, and 0.375 m. Adding these accurately ensures the final measurement is reliable and within tolerance limits.

Step-by-Step Solution

  1. Align the decimals: 0.125, 0.375, 0.375.
  2. Add column by column: 0.125 + 0.375 = 0.500.
  3. Then 0.500 + 0.375 = 0.875.
  4. The total length is 0.875 m.

Applying Conversions

To express this in centimetres, multiply by 100:

\(0.875 \times 100 = 87.5\text{ cm}\).

To three significant figures, the total length is 87.5 cm.

Common Mistakes

  • Failing to align decimal places before adding, which shifts place values incorrectly.
  • Misinterpreting units — e.g., adding metres and centimetres directly without converting first.
  • Rounding too early, which can distort final results in measurement-based problems.

Real-Life Connections

Engineers, scientists, and tradespeople routinely add decimals when working with precise measurements. For example:

  • Combining the thickness of metal sheets (0.312 m + 0.445 m + 0.118 m = 0.875 m).
  • Adding time intervals in data logging or timing experiments.
  • Summing fractional probabilities that must total 1.00.

Understanding how to handle decimals with care ensures results remain accurate across contexts.

FAQ

Q1: Should I round answers during intermediate steps?
A1: No — carry all decimals through until the final answer, then round to the specified precision.

Q2: Why use three decimal places here?
A2: Many scientific instruments measure to thousandths of a metre (millimetres), so accuracy at this level is realistic and useful for GCSE science integration.

Q3: Can I add decimals of different lengths (e.g., 0.2 + 0.125)?
A3: Yes. Pad with trailing zeros (0.200 + 0.125 = 0.325) so columns align correctly.

Study Tip

When adding or subtracting decimals in exam contexts, write all decimals to equal precision before starting. This avoids accidental column misalignment and helps when checking your answer with estimation.

Accurate decimal addition supports advanced GCSE topics such as proportional reasoning, significant figures, compound measures, and scientific notation. It also underpins calculator fluency for A-level science and engineering courses.