GCSE Maths Practice: place-value-and-rounding

Concept Overview

Rounding large numbers to the nearest thousand is essential when presenting population data, financial figures, or large-scale statistics. It allows comparisons to be made quickly without unnecessary detail. In GCSE Higher Maths, you may be asked not only to round but to interpret what the rounded values tell you about trends or differences. This question connects place value understanding with data analysis — a key skill tested in higher-tier reasoning and estimation tasks.

To round to the nearest thousand, you identify the thousands digit and check the hundreds digit to its right. If the hundreds digit is 5 or more, increase the thousands digit by 1. If it is 4 or less, keep the thousands digit the same. Replace all digits after the thousands place with zeros to reflect the level of rounding.

Step-by-Step Method

1. Locate the thousands and hundreds digits. Example: 67,423 → thousands = 7, hundreds = 4.
2. Apply the rounding rule. 4 < 5 → keep thousands = 7 → 67,000.
3. Repeat for the second dataset if needed. 67,610 → hundreds = 6 (≥5) → increase thousands to 8 → 68,000.
4. Interpret results. The rounded values indicate that the towns have approximately 67,000 and 68,000 residents — a difference of about 1,000 people.

Worked Examples

Example 1. Round 42,380 to the nearest thousand.

• Thousands = 2, hundreds = 3 → 42,000.

Example 2. Round 58,650 to the nearest thousand.

• Thousands = 8, hundreds = 6 → 59,000.

Example 3. Compare populations of 67,423 and 67,610.

• 67,423 → 67,000.
• 67,610 → 68,000.
• Rounded difference ≈ 1,000.

Common Mistakes

• Checking the wrong digit: Many students mistakenly look at the tens digit when rounding to thousands. The controlling digit is always the hundreds place.
• Writing 67,500: This is not a valid rounding because it implies rounding to the nearest 500, not the nearest thousand.
• Inconsistent rounding across data: When comparing two figures, round both to the same place value to ensure fairness.
• Overinterpreting rounded data: A rounded value hides small differences. Two towns with 67,001 and 67,499 both appear as 67,000 when rounded, though one is almost 500 higher.

Real-Life Applications

Government statistics, company revenue reports, and scientific studies often round to the nearest thousand to simplify communication. For instance, saying a population is “around 68 thousand” is more readable than “67,610.” In financial planning, annual profits might be shown as £68,000 rather than £67,610. The rounded figure provides clarity while remaining close enough for decisions that do not require extreme precision.

In exams, higher-tier questions often combine rounding with interpretation. After rounding, you might be asked whether the data suggest a meaningful change or whether the difference is within rounding error. This links directly to the concepts of accuracy and significant figures.

FAQ

Q1: Why is 67,500 not the correct answer?
A: Because the question asks for the nearest thousand. 67,500 would mean rounding to the nearest 500 instead, which isn’t a standard place value interval.

Q2: Why do we use the hundreds digit to decide?
A: It is the next digit to the right of the thousands place; it tells you whether the number is closer to the lower or upper thousand.

Q3: If two values round to the same thousand, does that mean they are identical?
A: No. It means their difference is less than 500, so they belong to the same rounding band but may still differ in reality.

Study Tip

Whenever comparing data, always round all numbers to the same place value before calculating or interpreting differences. Use number lines from one thousand to the next to visualise where the cut-off point (the midpoint, such as 67,500) lies. Understanding this prevents common rounding misinterpretations in data questions and prepares you for future topics like significant figures and error bounds.