Estimation and Approximation in Maths

An estimate is a sensible guess — a quick calculation that gives you a result that is close enough to be useful without being exact. Estimation is a critical skill for checking that answers are reasonable.

What Is the Difference Between Estimation and Approximation?

Estimation is a quick, informal calculation — you round numbers to make the arithmetic easier. Approximation is a more formal term for any value close to, but not exactly equal to, the true value. In everyday maths, the two words are often used interchangeably.

Rounding for Estimation

The most common way to estimate is to round numbers before calculating. Round to the nearest ten, hundred, or other convenient value depending on the required accuracy.

Front-End Estimation

In front-end estimation, you use only the leading (leftmost) digits of each number and replace the rest with zeros.

When to Estimate

• To check whether a calculated answer is sensible.
• When an exact answer is unnecessary (e.g. "is there enough money?").
• In science and engineering for quick feasibility checks.
• When shopping to avoid overspending.

Common Mistakes

• Rounding too aggressively and getting a very inaccurate estimate.
• Assuming an estimate is the exact answer.
• Forgetting to state that a value is an estimate (use ≈ to mean "approximately equal to").

Key Takeaways

Practice Questions

1. Estimate 389 + 512 by rounding to the nearest hundred.
2. Estimate 78 × 6 by rounding 78 to 80.
3. A cinema ticket costs £8.75. Estimate the cost of 9 tickets.
4. Use front-end estimation to estimate 741 − 268.
5. An answer of 42 000 was calculated for 69 × 82. Is this reasonable? Estimate to check.