Estimating means rounding every value in a calculation to $1$ significant figure before calculating, giving a quick, hand-calculable check on the size of an answer.

Find the first non-zero digit, look at the next digit to decide whether to round up or down, then replace everything else with placeholder zeros (keeping the decimal point sensibly placed). For example, $99.2$ rounds to $100$ at $1$ s.f. — this can look surprising, but it's correct, since the first significant digit is the $9$ in the tens place.

Round every number first, then substitute and simplify — often the rounded values are chosen (by the exam) to cancel neatly.

Worked Example

By rounding each number to $1$ significant figure, estimate the value of

1. Round each value to $1$ s.f.: $38.7\to40$, $99.2\to100$, $0.203\to0.2$, $4.87\to5$.
2. Substitute: $\dfrac{40+\sqrt{100}}{0.2\times5} = \dfrac{40+10}{1}$.
3. Evaluate: $\dfrac{50}{1}=50$.

An estimate is a fast, independent sanity check on a calculator answer. If you type a long expression and get $5.03$ back, but your $1$-s.f. estimate says the answer should be around $50$, you know instantly that a bracket or digit was mistyped — long before you'd notice from the number alone. Examiners deliberately design "estimate" questions to test this checking skill, not just arithmetic with rounded numbers.

Some real-world quantities can only take whole, sensible values, regardless of what the calculator displays — you must round to fit the context, not just to a stated number of decimal places, and you must always round in the sensible direction for the situation.

Worked Example

A minibus can carry $14$ passengers. $100$ people need transporting. How many minibuses are needed?

1. Divide: $100 \div 14 = 7.142857\ldots$
2. Rounding to $1$ decimal place would give $7.1$ minibuses — meaningless, since you can't send a fraction of a bus.
3. Since $7$ whole buses can't carry everyone, you must round up, regardless of how small the decimal part is: $8$ minibuses are needed.

Yes — even without an explicit calculation to round through, "estimate" still means using rounded, easy-to-handle values (often to the nearest convenient unit rather than strictly $1$ s.f.) to reach a quick approximate answer, rather than an exact calculated one. The underlying principle is always the same: trade a small amount of precision for a much faster, more manageable calculation.