Sensible Estimates
Get to grips with sensible estimates using these Foundation GCSE Maths practice questions. The worksheet focuses on choosing sensible estimates and units, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Match the unit to the object — a door is about 2 m tall.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Challenge / Extension
Stretch yourself beyond the basics.
Topic overview
A sensible estimate uses rounded values to produce an approximate answer quickly. It also means judging whether a measurement is plausible in real life.
For calculations, round each number to one significant figure and work mentally. For real-world judgement, compare the quantity against something familiar — a door is about \(2\)m tall, a bag of sugar is \(1\)kg, and a car is roughly \(4\)m long.
That second skill matters because it catches answers that are wildly wrong. If a calculation gives a person's height as \(17\)m, the arithmetic has failed somewhere, and noticing that is worth as much as the calculation itself.
Revision notes
Estimating calculations
Round each number to one significant figure, then calculate mentally.
So \(19.4 \times 4.8\) becomes \(20 \times 5 = 100\), which is close to the true value of \(93.12\).
Sensible real-world values
Compare against familiar benchmarks. A person is about \(1.7\)m tall, a bag of sugar is \(1\)kg, a mug holds about \(300\)ml.
Questions may ask you to pick the most sensible estimate from a list, so these reference points are worth knowing.
Choosing sensible units
Match the unit to the size of the quantity.
A room is measured in metres, a pencil in centimetres, and the distance between cities in kilometres. Using the wrong unit is a common error even when the number is right.
Key points
- Round to one significant figure to estimate.
- Compare real quantities against familiar benchmarks.
- A person is about 1.7m tall.
- A bag of sugar is about 1kg.
- Match the unit to the size of the quantity.
- Use estimates to check calculated answers.
Worked examples
Example 1
Estimate \(38.6 \times 5.2\).
Working
Example 2
Which is a sensible estimate for the height of a door: \(20\)cm, \(2\)m or \(20\)m?
Working
Example 3
Estimate \(\dfrac{412}{19.7}\).
Working
Common mistakes
Rounding to the nearest whole number instead of 1 significant figure.
412 becomes 400, not 412. One significant figure keeps only the first digit.
Accepting an implausible answer.
A person of height 17m signals an arithmetic error worth checking.
Using the wrong unit for the size of the quantity.
A room in millimetres or a pencil in metres is technically possible but not sensible.
Calculating exactly then rounding.
An estimate rounds first, then calculates mentally.
Exam tips
- Round first, then calculate mentally.
- Keep a few benchmark quantities in mind for comparison.
- Check every calculated answer against a rough estimate.
- Choose units that suit the size of what you are measuring.
Key terms
- Estimate
- An approximate answer using rounded values.
- Significant figure
- A digit contributing to accuracy, from the first non-zero digit.
- Benchmark
- A familiar quantity used for comparison.
- Plausible
- Reasonable for the real-life context.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.