GCSE Maths Practice: place-value-and-rounding

Question 4 of 9

This GCSE Higher question tests your ability to round accurately and apply that skill to a real-world estimation problem. You must round the price to the nearest hundred before calculating an approximate total, showing awareness of place value and estimation accuracy.

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\( \begin{array}{l}\text{A phone store sells 18 phones at an average price of }£1456.98.\\\text{Estimate the total revenue by rounding the price to the nearest hundred.}\end{array} \)

Choose one option:

Exam Tip: In multi-step estimation questions, always round before calculating. Avoid rounding twice or mixing precise and rounded values. Check your result is close to your mental estimate to confirm accuracy.

Try more: 23 items at £2347.80 each; 15 laptops at £984.60 each; 120 chairs at £148.20 each.

Concept Overview

Rounding to the nearest hundred is one of the key skills in GCSE Maths and appears in both Foundation and Higher Tier papers. While at Foundation level you may simply round a single number, at Higher level you are expected to apply rounding within multi-step problems. In business, science, and data analysis, rounding makes large or complex numbers easier to compare, estimate, and communicate. The decision to round up or down depends on the tens digit, which determines whether the number is closer to the lower hundred or the next one up.

In this problem, you are asked to round a monetary value before using it to estimate a total cost. This combination of rounding and reasoning transforms a basic skill into a Higher Tier application. Such questions test your ability to simplify real-world calculations while maintaining accuracy to a reasonable degree of precision.

Step-by-Step Method

  1. Identify the rounding place. For the nearest hundred, the hundreds digit is the key position. In £1456.98, the hundreds digit is 4.
  2. Find the next digit to the right. The tens digit is 5. This is the controlling digit that decides whether to round up or down.
  3. Apply the rounding rule. If the controlling digit is 5 or more, increase the rounding digit by 1. If it is less than 5, keep the rounding digit the same.
  4. Zero out all smaller place values. Replace the tens, ones, and any decimal places with zeros to show the number has been rounded to the nearest hundred.
  5. Use the rounded value in the wider context. In this example, multiply the rounded price by the number of phones to estimate the total revenue: 18 × £1500 = £27,000.

Worked Examples

Example 1. A laptop costs £2387.50. Round to the nearest hundred and estimate the cost of 6 laptops.

  1. Hundreds = 3; tens = 8 (≥5).
  2. Round up → £2400.
  3. Estimated total = 6 × £2400 = £14,400.

Example 2. A camera costs £1251.20. Round to the nearest hundred.

  1. Hundreds = 2; tens = 5 (≥5).
  2. Round up → £1300.

Example 3. A shop sells an item for £1456.98. Rounding to the nearest hundred gives £1500, which is then used for a quick mental estimate of total revenue. This type of reasoning often appears in real GCSE exam questions that ask you to check whether an answer is sensible or to estimate an overall cost.

Common Mistakes

  • Looking at the wrong digit. Many students mistakenly check the hundreds digit rather than the tens when rounding to the nearest hundred. Always look one place to the right of the rounding digit.
  • Forgetting to zero smaller places. If you write 1456 → 1450 instead of 1500, you have rounded to the nearest ten, not hundred.
  • Using inconsistent rounding in multi-step problems. Once you have rounded, all following calculations should use the rounded value, not the original figure.
  • Mixing up units. When working with money, always include the £ sign in the final answer to avoid losing marks.

Real-Life Applications

Rounding to the nearest hundred plays a key role in everyday numeracy. Businesses use it when estimating monthly revenue, project costs, or stock values. Scientists and engineers use it to simplify experimental data when full precision is unnecessary. In population studies or government statistics, figures are routinely rounded to the nearest hundred, thousand, or million to make reports more readable.

In GCSE Maths, rounding also supports the skill of estimation. Estimation questions often combine rounding with multiplication or division to help check whether an answer from a calculator is reasonable. For example, if you calculate 18 × 1456.98 = 26,225.64, you can confirm it is close to your rounded estimate of £27,000, showing that your exact calculation is sensible.

FAQ

Q1: Why do we round to the nearest hundred instead of keeping exact values?
Because real-world data is often uncertain or approximate. Rounding allows quick mental calculations without losing too much accuracy.

Q2: What happens if the tens digit is exactly 5?
Numbers halfway between two hundreds (e.g., 1450) always round up to the next hundred (1500).

Q3: Can I round again later in the question?
Only if instructed. Usually, you should perform all calculations using your first rounded value to keep results consistent.

Study Tip

Always check which digit controls the rounding. Highlight the rounding place and circle the digit to the right. This prevents confusion in multi-step questions. When estimating totals, round prices to the nearest hundred or thousand before multiplying — it saves time and keeps answers neat.