GCSE Maths Practice: place-value-and-rounding

Concept Overview

In manufacturing and quality control, products are often classified by rounded measurements. A part might be described as ‘1,000 mm’ long if its exact measurement rounds to 1,000 mm when rounded to the nearest hundred. Understanding which values qualify for a label or category requires logical reasoning with rounding rules. This type of question tests both your place-value understanding and your ability to apply mathematical reasoning to a practical context — an essential skill for higher-tier GCSE Maths.

To round to the nearest hundred, identify the hundreds digit and check the tens digit to its right. If the tens digit is 5 or more, the number rounds up. If it is less than 5, the hundreds digit stays the same. Replace the tens and ones digits with zeros to show the reduced precision. The range of numbers that round to 1,000 when rounded to the nearest hundred is from 950 up to (but not including) 1,050.

Step-by-Step Reasoning

1. Determine the rounding rule. Tens digit ≥ 5 → round up; less than 5 → stay the same.
2. Find the rounding range for 1,000. Numbers from 950 to 1,049.9... round to 1,000.
3. Check each candidate:
   • 920 → below 950 → rounds down to 900.
   • 998 → within 950–1,049 → rounds to 1,000.
   • 1,060 → above 1,049 → rounds up to 1,100.
   • 1,075 → above 1,049 → rounds up to 1,100.
4. Conclusion: Only 998 mm fits the rounding interval for 1,000 mm.

Worked Examples

Example 1. A label ‘1,000 ml’ is applied to bottles filled between 950 ml and 1,049 ml. Determine whether each batch passes inspection.

• Batch A: 920 ml → 900 → Fail.
• Batch B: 998 ml → 1,000 → Pass.
• Batch C: 1,060 ml → 1,100 → Fail.
• Batch D: 1,075 ml → 1,100 → Fail.

Example 2. Machine parts should be labelled 2,000 mm if they round to 2,000 when rounded to the nearest hundred. Find the acceptable range.

• Range = 1,950 mm ≤ length < 2,050 mm.

Common Mistakes

• Incorrect rounding boundaries. Many students think 1,050 still rounds to 1,000, but it actually rounds up to 1,100 because 50 counts as the midpoint.
• Using the thousands digit instead of hundreds. For the nearest hundred, always check the tens digit — not the ones or hundreds place.
• Rounding all numbers up automatically. Numbers below the midpoint must round down, even if they seem close to the upper target.
• Ignoring the range rule. To round to 1,000, the value must lie between 950 and 1,049 inclusive of the lower boundary.

Real-Life Applications

This kind of reasoning is essential in engineering, science, and product manufacturing. Dimensions, weights, and volumes are routinely rounded for categorisation. For example, a 998 ml bottle may be sold as “1 litre”, while 920 ml is labelled “900 ml.” Similarly, in construction, timber lengths may be described by rounded sizes like 1,000 mm or 2,400 mm, even though actual measurements vary slightly. Understanding these rounding rules ensures consistency and prevents mislabelling.

FAQ

Q1: What is the lowest number that rounds to 1,000 when rounded to the nearest hundred?
A: 950.

Q2: What is the highest number that rounds to 1,000?
A: 1,049 (anything 1,050 or higher rounds to 1,100).

Q3: Why does 998 count but 920 does not?
A: Because 998 is within 50 of 1,000, while 920 is more than 50 below the nearest hundred mark.

Study Tip

When asked which values round to a specific target, sketch the range visually on a number line. Mark the lower and upper cut-off points (here 950 and 1,049). Then check which numbers fall inside the interval. This method prevents common boundary errors and builds a deeper understanding of rounding intervals — an important bridge to the GCSE topic of error bounds and accuracy.