Estimation (Edexcel GCSE Maths): Revision Notes
Estimation
What is estimation?
Estimation is a method used to find an approximate answer to a calculation. This technique is particularly useful when you need to quickly check if your answer is reasonable, or when working on non-calculator exam papers where exact calculations would be too time-consuming.
The symbol ≈ means "approximately equal to" and is used throughout estimation work.
Basic estimation method
The fundamental approach to estimation follows these steps:
Essential Estimation Steps:
- Round each number to 1 significant figure
- Perform the calculation using the rounded values
- State that your answer is approximate
This method makes complex calculations much simpler while still giving you a good sense of what the answer should be.
Simple examples
Here are two straightforward examples to demonstrate the basic technique:
Worked Example 1:
- Round 4.32 to 4 (1 s.f.)
- Round 18.09 to 20 (1 s.f.)
- Calculate:
- Therefore:
Worked Example 2:
- Round 327 to 300 (1 s.f.)
- Calculate:
- Therefore:
Working with decimal divisions
When dividing by decimals, you can use a helpful trick to make estimation easier:
Decimal Division Trick: If you multiply both numbers in a division by the same amount, the answer stays the same.
For example:
This works because multiplying both the dividend and divisor by 100 eliminates the decimal without changing the final result.
Advanced estimation techniques
Using laws of indices
You can apply the laws of indices to estimate powers without a calculator:
This breaks down complex calculations into manageable parts by separating the significant digits from the powers of 10.
Working with formulas
When estimating with formulas, substitute rounded values for quick calculations:
Worked Example: Surface Area Estimation
For surface area of a sphere () with radius 2.35cm:
- Round to 3 and to 2
- Estimate: cm²
Understanding over and underestimates
It's important to recognise whether your estimate is higher or lower than the actual answer:
Types of Estimates:
- Underestimate: Your estimated answer is smaller than the true answer
- Overestimate: Your estimated answer is larger than the true answer
Compare your rounded numbers to the originals to determine which type of estimate you have.
Exam guidance
Key Exam Tips:
- Always show your rounding clearly in your working
- State whether your answer is an over or underestimate when asked
- Use estimation to check calculator answers for reasonableness
- Remember that can be rounded to 3 for quick estimates
Common exam requirement: Questions often ask you to "give a reason" for your answer - this means explaining whether you rounded up or down and how this affects your final estimate.
Practice approach
When practising estimation, follow these guidelines to develop strong technique:
Practice Guidelines:
- Write out your rounded calculation clearly
- Always use the symbol
- Double-check that you've rounded to 1 significant figure
- Consider whether your estimate makes sense in context
Remember!
Key Points to Remember:
- Estimation uses rounding to 1 significant figure followed by simple calculations
- The ≈ symbol indicates an approximate answer
- Show all your rounding steps clearly in exams
- Use estimation to check if calculator answers are reasonable
- Understand the difference between overestimates and underestimates for exam questions