GCSE Maths Practice: decimals

Question 7 of 10

This GCSE Higher-level question involves adding three decimal measurements and rounding to two decimal places. It develops accuracy, estimation, and understanding of place value in applied contexts.

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\( \begin{array}{1}\textbf{A runner completes three stages of a race measuring } 1.275\text{ km, } 2.846\text{ km, and } 1.259\text{ km.}\\ \text{Calculate the total distance, giving your answer correct to two decimal places.}\end{array} \)

Choose one option:

Estimate first to check your answer — 1 + 3 + 1 ≈ 5 km. Then add accurately and round correctly to two decimal places.

This Higher-tier GCSE Maths question challenges you to add decimals accurately and apply correct rounding rules to a contextual problem. Such problems are common in exam papers where measurement, accuracy, and interpretation all matter.

Scenario Context

A runner completes three stages of a long-distance race. The stage distances are 1.275 km, 2.846 km, and 1.259 km. To find the total distance covered, you must add all three decimal values and express the final result rounded to two decimal places.

Step-by-Step Solution

  1. Write the numbers vertically with decimal points aligned:
    1.275
    2.846
    1.259
  2. Add the hundredths column (5 + 6 + 9 = 20 → write 0, carry 2).
  3. Add the tenths and units carefully, carrying where needed: total = 5.380.
  4. Round to two decimal places → 5.38 km.

Checking for Reasonableness

Each stage is roughly between 1 km and 3 km. Estimating 1 + 3 + 1 ≈ 5 km confirms that 5.38 km is a sensible total.

Common Mistakes

  • Forgetting to align decimals, leading to misplaced place values.
  • Incorrect rounding (rounding 5.380 to 5.4 instead of 5.38).
  • Dropping trailing zeros, causing confusion when interpreting precision.
  • Misreading the question and failing to apply the rounding instruction.

Real-Life Applications

Decimal addition is vital for combining measurements, calculating costs, or analysing data. Examples include:

  • Adding fuel volumes in litres (12.35 L + 8.47 L = 20.82 L).
  • Summing time intervals recorded in seconds or minutes for experiments.
  • Combining probabilities or proportions in statistics and finance.

Advanced Thinking

At Higher level, you may also need to interpret the precision of each measurement. If the data were given to three decimal places, the result should reflect the same level of accuracy before rounding. This awareness of significant figures distinguishes a careful mathematician from one who only performs arithmetic.

Frequently Asked Questions

Q1: Why is the answer written as 5.38 rather than 5.380?
A1: When rounding to two decimal places, the third decimal digit (0) is dropped, giving 5.38. Writing 5.380 suggests three-decimal accuracy that wasn’t required.

Q2: Can I use a calculator for this type of problem?
A2: Yes, but you must still show alignment and rounding correctly. Examiners award marks for method and accuracy, not just the final number.

Q3: How can I check my answer without recalculating everything?
A3: Estimate. 1.3 + 2.8 + 1.3 ≈ 5.4, so 5.38 is very close and likely correct.

Study Tip

Always write one extra decimal place during working, then round at the end. This preserves accuracy and prevents cumulative rounding errors. When practising, use different contexts—distance, money, weight—to strengthen your versatility with decimal operations.

Mastering decimal addition with rounding prepares you for more advanced GCSE topics such as density calculations, compound measures, and proportional reasoning where precision and estimation go hand in hand.