GCSE Maths Practice: estimation

Using Significant Figures in Estimation

Estimation using significant figures is one of the quickest and most accurate ways to check answers in GCSE Maths. When you round each number to one significant figure, the multiplication becomes simple enough to do mentally while keeping the result close to the real value.

Why Use Significant Figures?

Significant figures capture the most important digits of a number — those that actually influence its size. By rounding 13.8 to 10 and 7.6 to 8, we keep the essential scale of both numbers but make the operation easier. This prevents calculation errors and reinforces your sense of number size.

Step-by-Step Estimation Method

1. Look at the first non-zero digit. That’s the first significant figure.
2. Check the next digit to decide whether to round up or down.
3. Replace remaining digits with zeros to simplify the number.
4. Perform the operation mentally using the rounded values.

Worked Examples

Example 1:
13.8 × 7.6 → 10 × 8 = 80
Exact product = 104.88, so the estimate is close enough to check reasonableness.

Example 2:
42.9 × 3.2 → 40 × 3 = 120
Exact answer = 137.28 — only slightly higher than the estimate.

Example 3:
0.86 × 24.5 → 1 × 20 = 20
Exact result = 21.07. The rounded version gives the same order of magnitude.

Common Errors to Avoid

• Rounding incorrectly when the next digit is 5 or more.
• Using too many significant figures, which defeats the purpose of estimation.
• Forgetting to apply the same rounding logic to both numbers before multiplying.
• Confusing significant figures with decimal places — they measure different things.

Real-World Application

Significant figure estimation is vital in science, engineering, and finance. For example, a builder estimating materials might multiply 13.8 m by 7.6 m to find the area of flooring. Rounding to 10 × 8 gives 80 m², a fast and practical estimate for planning purchases before making exact measurements.

Quick FAQs

• Q: What’s the difference between rounding to 1 s.f. and rounding to 1 decimal place?
  A: 1 s.f. focuses on the most important digit, while 1 decimal place keeps only one digit after the decimal point.
• Q: When is it best to round to 2 significant figures?
  A: When greater accuracy is required but you still want to simplify calculations.
• Q: Is the estimate always lower than the true answer?
  A: Not necessarily — it depends whether numbers were rounded up or down.

Study Tip

When working under time pressure, round both numbers to 1 s.f. and multiply mentally. This gives you a quick check to ensure your final calculator result is logical.

Summary

Estimation with significant figures is a crucial foundation for mental arithmetic. It enhances accuracy awareness and helps you judge whether your detailed results make sense in GCSE Maths and beyond.