GCSE Maths Practice: decimals

Question 1 of 10

This Higher-level question mixes multiple decimal operations — addition, subtraction, multiplication, and rounding — demanding precision and structured working throughout.

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\( \begin{array}{l}\text{Calculate (1.235 + 0.478 - 0.295)}\times 1.91, \text{ giving your answer to two d.p.}\end{array} \)

Choose one option:

Estimate before working — around 2.8 expected — then check carefully with each step. Always leave rounding to the end.

This Higher-tier GCSE Maths question extends decimal arithmetic to several combined operations, including rounding to specified accuracy. It demands attention to place value and order of operations rather than just single-step computation.

Scenario Context

An engineer records three small measurements in metres: 1.235, 0.478, and 0.295. After adjusting for calibration, the corrected total is multiplied by 1.91 to account for scale. The task is to find the final scaled value, rounded to two decimal places.

Step-by-Step Method

  1. Addition: Combine 1.235 and 0.478 carefully, aligning decimal points → 1.713.
  2. Subtraction: 1.713 − 0.295 = 1.418. Writing decimals vertically helps avoid place-value errors.
  3. Multiplication: Multiply 1.418 × 1.91. Ignore the decimals at first (1418 × 191 = 270738), then place four decimals → 2.70738.
  4. Rounding: Two decimal places means keep the hundredths column → 2.71.

Accuracy and Order

Perform operations in the correct order: addition and subtraction first, then multiplication. Using brackets or separate steps ensures correct sequencing when calculators are unavailable.

Common Mistakes

  • Forgetting to align decimal points when adding or subtracting.
  • Rounding too early (before multiplication), causing cumulative errors.
  • Miscounting decimal places after multiplication — especially when one factor has two decimals and the other has three.
  • Dropping trailing zeros that help track precision.

Worked Example

Example: (0.84 + 0.275 − 0.06) × 1.5

Step 1: 0.84 + 0.275 = 1.115
Step 2: 1.115 − 0.06 = 1.055
Step 3: 1.055 × 1.5 = 1.5825 → Rounded = 1.58

This demonstrates the same pattern: combine decimals accurately, then scale.

Checking and Estimation

Estimation helps verify reasonableness. Here, (1.2 + 0.5 − 0.3) ≈ 1.4, and 1.4 × 2 ≈ 2.8 — close to the final answer 2.71, confirming it’s plausible.

Real-Life Applications

  • Adjusting small sensor readings in engineering or science.
  • Scaling dimensions or weights with correction factors.
  • Budgeting calculations involving small amounts multiplied by rates.

FAQ

Q1: Why is rounding left until the end?
A1: Because rounding early loses precision. GCSE mark schemes reward correct rounding at the final stage only.

Q2: Can I use a calculator?
A2: Yes, but write down intermediate results clearly to show understanding.

Q3: How do I know where to place the decimal after multiplication?
A3: Count the total number of decimal places in both factors and move the decimal point that many places left.

Study Tip

When several decimal operations appear together, always estimate before each operation. This builds a mental check that protects against misplaced decimals — one of the most common Higher paper errors.

This kind of multi-step decimal problem reflects the precision expected in higher-level GCSE calculations and links directly to later topics like compound measures and percentage change.