GCSE Maths Practice: place-value-and-rounding

Question 2 of 10

This question checks whether each given rounding result is correct when rounding to the nearest hundred. Examine each number carefully and look at its tens digit before deciding if it should round up or down.

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

Select all correct options:

Exam tip: Draw a short number line for each question. For 7400, the range is 7350–7449. Any number within that interval rounds to 7400. This visual approach ensures 100% accuracy in exams.

Try more: 4635, 8209, 5901.

Concept Overview

When rounding to the nearest hundred, the tens digit decides what happens to the hundreds digit. If the tens digit is 5 or greater, you round the hundreds digit up. If the tens digit is 4 or less, you keep the hundreds digit the same and replace all digits to the right with zeros. This keeps your number neat and accurate for estimation.

In this question, you must decide whether the given rounding results are correct. This means checking how each number behaves when applying the rounding rule.

Step-by-Step Method

  1. Identify the hundreds and tens digits. These two places determine what rounding does to the number.
  2. Apply the rounding rule. Compare the tens digit to 5. If it’s 5 or more, the hundreds digit increases by one. If it’s smaller, the hundreds digit stays the same.
  3. Replace all digits to the right of the hundreds place with zeros.
  4. Check your rounded value against the answer given.

Worked Examples

Example 1: Round 672 to the nearest hundred.

  • Hundreds = 6; tens = 7 ( ≥ 5 ) → round up.
  • Answer: 700.

Example 2: Round 4,318 to the nearest hundred.

  • Hundreds = 3; tens = 1 ( < 5 ) → round down.
  • Answer: 4,300.

Example 3: Round 950 to the nearest hundred.

  • Hundreds = 9; tens = 5 ( ≥ 5 ) → round up → 1000.
  • Answer: 1000.

Example 4: Round 7425 to the nearest hundred.

  • Tens = 2 ( < 5 ) → round down → 7400.

Common Mistakes

  • Automatically rounding up: Not every number rounds up — check the tens digit first.
  • Wrong number of zeros: When rounding to the nearest hundred, the last two digits must be zeros.
  • Rounding the wrong place: Some learners accidentally round to the nearest ten instead of hundred — always identify which place value the question specifies.

Real-Life Applications

Rounding to the nearest hundred is helpful in many everyday tasks:

  • Money: If an item costs £7425, it’s approximately £7400 — useful when comparing large budgets.
  • Distance: A journey of 8431 metres is about 8400 metres, or roughly 8.4 km.
  • Population: If a town has 5012 people, you might report it as “about 5000.”

FAQ

Q1: Why does 8431 not round to 8500?
A: Because the tens digit is 3, which is less than 5. Therefore, we round down to 8400.

Q2: Why do 7425 and 5012 round down?
A: Both have tens digits smaller than 5, meaning they stay at their current hundred level.

Q3: What happens when the hundreds digit becomes 10?
A: If rounding makes the hundreds digit reach 10, it increases the next place — for example, 950 → 1000.

Study Tip

When checking multiple numbers, underline the hundreds and tens digits. This quick visual guide helps you apply the rounding rule accurately without confusion. If the tens digit is 0–4, write “down”; if it’s 5–9, write “up.”