GCSE Maths Practice: place-value-and-rounding

Question 4 of 10

This foundation question checks your ability to round large numbers to the nearest thousand. The hundreds digit decides whether the thousands digit increases or stays the same. Be careful not to confuse the hundreds and tens digits.

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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: Always underline the hundreds digit before rounding — it’s the key to knowing which thousand the number belongs to. The rule: 0–4 round down, 5–9 round up.

Try more: 1599, 2750, 8649.

Concept Overview

Rounding to the nearest thousand is a practical way to simplify large numbers for easier comparison or estimation. You determine whether to round up or down by looking at the hundreds digit. If that digit is 5 or more, increase the thousands digit by 1. If it is 4 or less, keep the thousands digit the same and replace all digits to the right with zeros.

Rounding is especially useful in real-life contexts such as budgeting, population data, or measurement estimates, where exact values are unnecessary.

Step-by-Step Method

  1. Identify the hundreds digit — it determines the rounding direction.
  2. Apply the rounding rule:
    • If the hundreds digit ≥ 5 → round up.
    • If the hundreds digit ≤ 4 → round down.
  3. Replace smaller place values (hundreds, tens, and ones) with zeros.
  4. Write the new rounded number — it should always end in three zeros.

Worked Examples

Example 1: Round 6421 to the nearest thousand.

  • Thousands = 6; hundreds = 4 (< 5).
  • Round down → 6000.

Example 2: Round 8299 to the nearest thousand.

  • Thousands = 8; hundreds = 2 (< 5).
  • Round down → 8000.

Example 3: Round 19350 to the nearest thousand.

  • Thousands = 19; hundreds = 3 (< 5).
  • Round down → 19000.
  • The claim “19350 → 20000” is incorrect.

Common Mistakes

  • Checking the wrong digit: Many learners mistakenly look at the tens digit instead of the hundreds digit when rounding to the nearest thousand.
  • Forgetting zeros: Remember to replace all digits after the rounding place with zeros for a clean result.
  • Assuming mid-values always round up: Only numbers with a hundreds digit of 5 or greater round up — 19350 rounds down because its hundreds digit (3) is less than 5.

Real-Life Applications

Rounding large numbers makes data and everyday figures easier to understand:

  • Money: £6,421 ≈ £6,000 for a rough budget estimate.
  • Population: A town of 8,299 people is about 8,000 in population studies.
  • Distance: 19,350 metres ≈ 19,000 metres (or 19 km) when measuring roughly.

FAQ

Q1: Why does 19,350 not round to 20,000?
A: Because the hundreds digit (3) is below 5, so we round down to 19,000.

Q2: What if the number was 19,550?
A: Then it would round up to 20,000, since the hundreds digit (5) means “round up.”

Q3: What’s the halfway point when rounding thousands?
A: 500 marks the halfway point (e.g., between 6000 and 7000, the midpoint is 6500).

Study Tip

Use a number line between 19,000 and 20,000. The midpoint 19,500 helps you visualise when rounding changes direction. Anything below 19,500 rounds down, and anything 19,500 or above rounds up.