GCSE Maths Practice: place-value-and-rounding

Question 3 of 10

This foundation question checks your skill in rounding large numbers to the nearest thousand. Focus on the hundreds digit — it tells you whether to round up or down.

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\( \begin{array}{l}\text{Which of the following rounding results are correct to the nearest thousand?}\end{array} \)

Select all correct options:

Exam tip: When rounding to the nearest thousand, write 500 as your halfway point on a quick sketch line. Anything from 0–499 rounds down; 500–999 rounds up. This makes large-number rounding effortless under time pressure.

Try more: 1,345, 9,650, 27,499.

Concept Overview

Rounding to the nearest thousand is an essential skill for simplifying large numbers in everyday life and data analysis. To decide which thousand a number is closest to, you must look at the hundreds digit. If the hundreds digit is 5 or greater, the thousands digit increases by 1. If the hundreds digit is 4 or lower, the thousands digit stays the same. All digits to the right are replaced with zeros.

For example, in the number 7,845:

  • The thousands digit is 7.
  • The hundreds digit is 8 (≥ 5).
  • Since the hundreds digit is 8, we round up to 8,000.

Step-by-Step Method

  1. Identify the thousands and hundreds digits. These two digits control the rounding process.
  2. Compare the hundreds digit with 5. If it is 5 or more, round up. If it is 4 or less, round down.
  3. Replace lower place values (hundreds, tens, and ones) with zeros.
  4. Write the rounded value. The result should always end with three zeros when rounding to the nearest thousand.

Worked Examples

Example 1: Round 2,456 to the nearest thousand.

  • Thousands = 2; hundreds = 4.
  • Since 4 < 5, round down.
  • Answer: 2,000.

Example 2: Round 7,845 to the nearest thousand.

  • Thousands = 7; hundreds = 8.
  • Since 8 ≥ 5, round up.
  • Answer: 8,000.

Example 3: Round 36,789 to the nearest thousand.

  • Thousands = 36; hundreds = 7.
  • Since 7 ≥ 5, round up.
  • Answer: 37,000.

Common Mistakes

  • Rounding based on the tens digit: For thousands rounding, only the hundreds digit matters — not the tens or ones.
  • Forgetting zeros: Replace all digits after the thousands place with zeros for a clean, accurate result.
  • Rounding in the wrong direction: Always check carefully if the hundreds digit is below or above 5 before deciding.

Real-Life Applications

Rounding to the nearest thousand is common in:

  • Population counts: A town with 36,789 people is approximately 37,000.
  • Finance and business: £7,845 can be rounded to £8,000 for easy budgeting.
  • Distance and travel: A journey of 2,456 metres is roughly 2,000 metres, or 2 km.

FAQ

Q1: Why does 2,456 round to 2,000 and not 3,000?
A: Because the hundreds digit (4) is less than 5, so we keep the thousands digit as it is.

Q2: What happens when the hundreds digit is exactly 5?
A: It always rounds up. For example, 2,500 → 3,000.

Q3: What if the number is 9999?
A: It rounds up to 10,000, because the hundreds digit (9) is greater than 5.

Study Tip

Draw a quick number line between two thousands — for example, between 2,000 and 3,000. Mark the midpoint (2,500). Numbers below 2,500 round down; numbers 2,500 and above round up. This simple visual helps make rounding much easier to understand in exams and real-life estimation.