GCSE Maths Practice: place-value-and-rounding

Question 3 of 9

This GCSE Higher problem uses rounding in a real-life manufacturing context. You must round to the nearest ten before estimating how many containers are required — a typical multi-step estimation skill tested in non-calculator papers.

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\( \begin{array}{l}\text{A factory produces }1,923\text{ parts in one day. Each crate holds }10\text{ parts.}\\\text{Round the total to the nearest ten and estimate how many crates are needed.}\end{array} \)

Choose one option:

Exam tip: When the question involves words like estimate or approximately, always round first, then compute mentally or with minimal working. Checking that your rounded result makes sense earns method marks even if the final total differs slightly from the exact answer.

Try more: 2,368 items in boxes of 10; 7,842 bolts per shipment; 1,925 students per bus fleet.

Concept Overview

Rounding to the nearest ten allows quick estimation when exact values are unnecessary. In GCSE Higher Maths, this skill is often integrated into multi-step, real-world problems such as calculating quantities, costs, or capacities. You must decide when to round, apply the correct rule, and then use that rounded value sensibly in a subsequent calculation. This type of question tests your fluency with place value, logical reasoning, and efficiency in estimation.

In this scenario, a factory produces 1,923 parts in one day, and each crate can hold 10 parts. Rather than performing long calculations using the precise number, we can round 1,923 to the nearest ten to obtain a quick, reliable estimate of how many crates are required. Such reasoning appears frequently in higher-tier non-calculator papers, where you must show a justified estimate rather than an exact figure.

Step-by-Step Method

  1. Identify the rounding place: The tens place controls how we group numbers into convenient multiples of ten. Here, the tens digit is 2.
  2. Check the next digit (ones place): The ones digit is 3. Because 3 < 5, we round down and keep the tens digit as it is.
  3. Zero the smaller places: Replace the ones digit with 0 → 1,920.
  4. Use the rounded number in the wider calculation: 1,920 ÷ 10 = 192 crates (an estimate).

Worked Examples

Example 1. A bakery makes 2,368 rolls. Each tray holds 10. Round to the nearest ten to estimate the number of trays.

  1. Ones = 8 (≥5) → round up: 2,370.
  2. 2,370 ÷ 10 = 237 trays (approx.).

Example 2. A company packs 7,842 screws in boxes of 10. Round to the nearest ten.

  1. Ones = 2 (<5) → 7,840.
  2. 7,840 ÷ 10 = 784 boxes.

Example 3. A school prints 1,923 exam papers. Bundles hold 10 each. Round and estimate bundles needed.

  1. 1,923 → 1,920.
  2. 1,920 ÷ 10 = 192 bundles.

Common Mistakes

  • Rounding before identifying the place correctly: Some students mistakenly look at the hundreds digit instead of the ones when rounding to the nearest ten.
  • Forgetting to apply the rounded number in context: The question often requires an additional calculation after rounding.
  • Rounding twice: Once you have rounded, use that number consistently to avoid compounding error.
  • Neglecting reasonableness checks: Always ask if your estimate is sensible compared to the exact figure.

Real-Life Applications

Rounding to the nearest ten is used daily in production, packaging, budgeting, and scheduling. Manufacturers round quantities to plan shipping boxes or pallets. Retailers round sales figures to tens or hundreds for summary reports. In scientific work, data may be rounded to appropriate precision to reflect the accuracy of measuring instruments. These examples mirror the logic of this question—simplifying data for practical decision-making without significant loss of accuracy.

FAQ

Q1: Why do we round before dividing by 10?
A: Because rounding simplifies the dividend, making the division mental and faster, while still keeping the result close to the exact answer.

Q2: What if the ones digit is exactly 5?
A: Numbers ending in 5 always round up. For instance, 1,925 → 1,930.

Q3: Will rounding up ever make my estimate too large?
A: Possibly, but in estimation questions, you justify that your result is reasonable, not exact. Slight over- or under-estimates are acceptable if logically explained.

Study Tip

In multi-step problems, highlight the instruction words: round, estimate, calculate, justify. They tell you when to switch from exact arithmetic to approximate reasoning. Practise rounding numbers like 1,237, 5,946, and 9,872 to the nearest ten or hundred, then apply those values in short word problems. This builds the flexible numerical sense required for top GCSE grades.