Using Estimation
Ever checked if a calculation on your phone seems sensible, or wanted a quick idea of the total cost in a shop? That’s estimation! It’s about finding a sensible, rough answer quickly by rounding numbers before you calculate.
Understanding Significant Figures
For GCSE, you will usually estimate by rounding to one significant figure. The first significant figure is the first non-zero digit in a number, reading from left to right.
Example 1: 428
428
The first significant figure is 4.
Example 2: 0.00619
0.00619
The first significant figure is 6.
How to Round to One Significant Figure
- Identify the first significant figure.
- Look at the digit immediately to its right.
- Apply the rule: If the next digit is 5 or more, round the first digit up. If it’s 4 or less, keep it the same.
- Replace all other digits with zeros to keep the place value.
The first digit is 3. The next digit is 7 (so round up).
Answer: 400
The first significant figure is 4. The next is 3 (so the 4 stays the same).
Answer: 0.04
Worked Examples: Estimating Calculations
Example 1: Multiplication
Estimate the answer to $53 \times 8.7$.
- Round each number to 1 s.f.:
$53 \approx 50$
$8.7 \approx 9$ - Perform the estimated calculation:
$50 \times 9 = 450$.
Estimated Answer: 450
(Exact answer: 461.1)
Example 2: Division
Estimate the answer to $612 \div 29$.
- Round each number to 1 s.f.:
$612 \approx 600$
$29 \approx 30$ - Perform the estimated calculation:
$600 \div 30 = 20$.
Estimated Answer: 20
(Exact answer: approx 21.1)
Tutor Insights
🤔 Common Misunderstandings
- Maintaining place value: A common error is rounding 372 to 4 instead of 400. You must replace the other digits with zeros!
- Identifying the first significant figure: Especially with decimals like 0.007 (where 7 is the first s.f.). Remember that leading zeros don’t count.
📝 Common Exam Mistakes
- Not showing the rounded numbers: You must write down your rounded numbers (e.g., $600 \div 30$) before the final answer to get method marks.
- Rounding incorrectly: A simple slip in the rounding rule will lead to an incorrect estimate.
Practice Questions
- Estimate the answer to $68 \times 3.2$ by rounding each number to one significant figure.
- Estimate the answer to $412 + 789$.
- Estimate the answer to $207 \div 4.8$.
- Estimate the answer to $\frac{78.2 + 21.5}{4.9}$.
Show Answers
- Working: $70 \times 3 = \mathbf{210}$.
- Working: $400 + 800 = \mathbf{1200}$.
- Working: $200 \div 5 = \mathbf{40}$.
- Working: Numerator $\approx 80 + 20 = 100$. Denominator $\approx 5$. So, $100 \div 5 = \mathbf{20}$.
FAQs
Why do we always round to *one* significant figure for estimation?
A: Rounding to one significant figure simplifies numbers the most, making calculations quick and easy to do mentally. Unless a question asks for a different level of accuracy, assume one significant figure for estimation questions.
Is it okay if my estimate is really different from the exact answer?
A: Yes, within reason! The goal is to get an answer in the right ballpark to check if your exact answer is sensible. If the exact answer is 461 and your estimate is 450, that’s great. If your estimate is 45, something’s gone wrong.
