Round to a given number of decimal places or significant figures; estimate calculations by rounding to one significant figure; and find upper and lower bounds and use them in calculations (Higher tier).

What this dot point is asking

The Eduqas number content closes with rounding, estimation and bounds. You must round to a stated number of decimal places or significant figures, estimate the answer to a calculation by rounding each value to one significant figure, and (at Higher tier) find the upper and lower bounds of a rounded measurement and combine them in calculations such as area, speed and density. Estimation appears on the non-calculator Component 1 as a sense check, while bounds is a Higher reasoning topic that examiners use to test careful, structured thinking.

Rounding to decimal places and significant figures

Rounding replaces a number with a nearby, simpler one.

To round to a number of decimal places, count that many digits after the decimal point and look at the next digit: $3.6472$ to $2$ decimal places is $3.65$ (the next digit, $7$, rounds up). To round to significant figures, start counting from the first non-zero digit: $0.0048213$ to $2$ significant figures is $0.0048$, and $52\,830$ to $2$ significant figures is $53\,000$. The rounding rule is the same throughout: $5$ or more rounds up, $4$ or less rounds down.

Estimating calculations

A one-significant-figure estimate gives a quick check on a calculator answer.

To estimate, round every number to one significant figure, then do the easier calculation: $\dfrac{41.7 \times 19.3}{5.8} \approx \dfrac{40 \times 20}{6} = \dfrac{800}{6} \approx 133$. The estimate need not be exact; it confirms the order of magnitude and catches gross errors. Dividing by a number less than $1$ makes the result larger, which is a frequent source of surprise, so $\dfrac{50}{0.5} = 100$, not $25$.

Upper and lower bounds (Higher)

A rounded measurement hides a range of possible true values.

When bounds are combined in a calculation, the choice of bound depends on the operation. For a sum or product, the largest result uses the upper bounds of both inputs. For a difference or quotient, the largest result uses the upper bound of one and the lower bound of the other.

Why this matters

Estimation is the habit that catches a misplaced decimal point or a wrong calculator entry, which is why Eduqas embeds it on the non-calculator component. Bounds formalise the idea that every measurement carries uncertainty, a genuinely scientific concept, and the bounds questions are pure AO2 and AO3 reasoning: choosing which bound to use for the largest or smallest result tests whether you understand the structure of the calculation, not just how to round.