Round to a given number of decimal places or significant figures; estimate calculations; and find and use upper and lower bounds, including in calculations (Higher tier).

What this dot point is asking

OCR references N5 and N15 cover rounding to decimal places and significant figures, estimating calculations by rounding, and at Higher tier finding and using upper and lower bounds. These are the tools for handling measurement and approximation: real quantities are never exact, and a measured value carries a margin of error you can quantify. Estimation is tested on the non-calculator paper as a check on calculator answers, while bounds are a reliably tricky Higher topic.

Rounding to decimal places and significant figures

Both kinds of rounding use the same decision rule but count from a different place.

So $3.14159$ to $2$ d.p. is $3.14$, and to $3$ s.f. is also $3.14$. But $0.004072$ to $2$ s.f. is $0.0041$ (the first significant figure is the $4$), and $48\,620$ to $2$ s.f. is $49\,000$ (the trailing zeros hold place value). Watch the carry: $9.97$ to $1$ d.p. rounds to $10.0$, because the $9$ tenths round up.

Estimating calculations

Estimation gives a quick sanity check and is examined in its own right.

To estimate, round every number to one significant figure and work with the friendly values. This catches calculator slips: if your machine says a bill is £$1240$ but the estimate is £$120$, you have a factor-of-ten error somewhere. The notation $\approx$ ("approximately equal to") signals an estimate. The awkward case is dividing by a small decimal: dividing by $0.2$ multiplies by $5$, so estimates involving small divisors get large.

Bounds (Higher)

Every rounded measurement hides a range of true values.

To get the extreme value of a calculation, choose bounds carefully. A sum or product is largest when both inputs are at their upper bound. A difference $a - b$ is largest when $a$ is at its upper bound and $b$ at its lower bound. A quotient $\tfrac{a}{b}$ is largest when $a$ is at its upper bound and $b$ at its lower bound, because dividing by a smaller number gives more.

Why bounds matter

Bounds turn "measured roughly" into a precise statement about the possible answer, which OCR uses to test reasoning (AO2) as much as calculation. They tie directly into compound measures such as speed and density, where each measured quantity carries its own margin. A frequent Higher question asks you to find both bounds of an answer and then state it "to a suitable degree of accuracy", which means quoting the digits the upper and lower bounds agree on.