GCSE Maths Practice: place-value-and-rounding

Concept Overview

Rounding to the nearest hundred is widely used in financial reporting and budgeting. When figures are in the thousands, rounding helps simplify communication while retaining a realistic sense of scale. In GCSE Higher Maths, this kind of question often links rounding with estimation or multiplicative reasoning, asking you to apply rounded values to a follow-up calculation. Here, the figure £5,387.99 represents a company’s monthly sales; rounding allows an efficient estimate for longer time periods without complex arithmetic.

Rounding to the nearest hundred means focusing on the hundreds digit and checking the tens digit. If the tens digit is 5 or greater, increase the hundreds digit by 1. If it’s 4 or less, keep it the same. Replace all smaller digits with zeros to show the level of precision clearly. This rule ensures consistency whether dealing with money, population, or measurements.

Step-by-Step Method

1. Identify the rounding place. Hundreds digit = 3, tens digit = 8.
2. Decide the rounding direction. 8 ≥ 5 → round up → hundreds digit becomes 4.
3. Write zeros for smaller places. Result = £5,400.
4. Apply the rounded value in a context. If monthly sales ≈ £5,400, then six months ≈ 6 × £5,400 = £32,400.
5. Compare to the exact total. Exact: 6 × £5,387.99 = £32,327.94 → Estimate is close and sensible.

Worked Examples

Example 1. Round £5,387.99 to the nearest hundred and estimate 6 months of sales.

• £5,387.99 → £5,400.
• 6 × £5,400 = £32,400.
• Estimated total = £32,400.

Example 2. Round £2,349.60 to the nearest hundred and estimate a 12-month total.

• £2,349.60 → £2,300.
• 12 × £2,300 = £27,600 (approx).

Example 3. Round £6,151.90 to the nearest hundred for budgeting.

• Hundreds = 1; tens = 5 → round up → £6,200.

Common Mistakes

• Rounding after multiplying. For estimation, round before calculating to make the numbers easier to handle.
• Rounding to the wrong place. When asked for the nearest hundred, ensure your answer ends with two zeros (e.g., 5,400 not 5,000).
• Omitting currency symbols. In money questions, always include £ for clarity and to reinforce real-world meaning.
• Over-precision in estimates. Avoid writing long decimals when estimating; stick to the rounded figures throughout.

Real-Life Applications

Businesses regularly use rounded figures for forecasts and presentations. A sales manager might report “approximately £5,400 per month” rather than £5,387.99 to avoid unnecessary detail. Similarly, construction budgets, project quotes, and financial summaries use rounded values to the nearest hundred or thousand for clarity. Even small rounding differences (within about 1–2%) are acceptable in estimation contexts because they do not significantly affect decision-making.

FAQ

Q1: Why round before multiplying?
A: It simplifies calculations and reduces cognitive load. The small error caused by rounding is acceptable when only an estimate is needed.

Q2: Is it better to round up or down in financial estimates?
A: It depends on context: round up when budgeting to ensure coverage, round down for conservative sales estimates.

Q3: Why must rounded hundreds end with two zeros?
A: Because tens and ones are no longer significant; they are replaced with zeros to show the loss of precision.

Study Tip

When performing multi-step calculations, highlight the instruction words: round, estimate, and calculate. Always show both the rounding step and the final estimated calculation—examiners give credit for reasoning even if your arithmetic is slightly off. Practise converting decimals into rounded financial figures quickly so you can focus on the reasoning in multi-step word problems.