GCSE Maths Practice: place-value-and-rounding

Question 5 of 9

This question challenges you to round a large number to the nearest thousand. Understanding how place value affects rounding helps in estimation, statistics, and large-scale calculations.

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\( \begin{array}{l}\text{Round }12,345\text{ to the nearest thousand.}\end{array} \)

Choose one option:

Common mistake: Increasing the thousands digit when the hundreds digit is less than 5. Always check the hundreds digit before deciding.

Try more: 18,620; 32,499; 67,850.

Concept Overview

Rounding to the nearest thousand means finding the multiple of 1,000 that is closest to a given number. We use it to simplify large values so they are quicker to read, compare, and estimate with. In everyday contexts such as budgeting, scientific measurement, and population statistics, rounded numbers communicate scale clearly while staying close to the exact value. The decision to round a number up or down depends on the digit immediately to the right of the place value we are rounding to. For the nearest thousand, that controlling digit is the hundreds digit.

3-Step Method (Nearest Thousand)

  1. Locate the thousands digit and the hundreds digit.
  2. Decide: if the hundreds digit is 5 or more, increase the thousands digit by 1; if it is less than 5, keep it the same.
  3. Zero all digits to the right of the thousands place.

Worked Examples

Example 1. Round 16,720 to the nearest thousand.

  1. Thousands = 6; hundreds = 7.
  2. Since 7 ≥ 5, increase thousands to 7.
  3. Answer: 17,000.

Example 2. Round 45,230 to the nearest thousand.

  1. Thousands = 5; hundreds = 2.
  2. Since 2 < 5, keep thousands = 5.
  3. Answer: 45,000.

Example 3. Round 89,550 to the nearest thousand.

  1. Thousands = 9; hundreds = 5.
  2. Since 5 ≥ 5, round up.
  3. Answer: 90,000.

Common Mistakes

  • Using the wrong controlling digit. For nearest thousand, look at the hundreds digit (not the tens).
  • Changing the thousands digit when the hundreds digit is less than 5. If the hundreds digit is 0–4, the thousands digit stays the same.
  • Forgetting to replace lower place values with zeros. After rounding to the nearest thousand, the hundreds, tens, and ones must be 0.
  • Rounding in two stages. Do not round to the nearest hundred and then to the nearest thousand; round once directly to the target place value.

Real-Life Applications

Rounding to the nearest thousand appears in many real scenarios: companies round revenue to the nearest £1,000 for quick comparisons; scientists may round experimental counts to avoid implying unrealistic precision; government reports often use rounded population figures. In exams, rounding lets you estimate before calculating exactly, which is useful for checking whether an answer is sensible.

FAQ

Q: What if the hundreds digit is exactly 5?
A: Round up. For example, 12,500 → 13,000.

Q: Why do we write zeros after rounding?
A: Because rounding to the nearest thousand removes information below the thousands place. Those lower places are no longer significant and must be set to zero.

Q: Does rounding always make the number bigger?
A: No. If the hundreds digit is 0–4 you round down (or stay the same), and if it is 5–9 you round up.

Try More

Practise with: 18,620; 32,499; 67,850; 101,499; 250,501. Check your decisions by focusing on the hundreds digit each time.

Revision Tip

Think of 5 as the turning point: 0–4 → keep the thousands digit; 5–9 → add one to the thousands digit. Then zero everything to the right.