Choose bounds for biggest or smallest
For a sum/product use both upper (or both lower); for a difference/quotient mix them: UB(a−b)=UB(a)−LB(b), UB(a÷b)=UB(a)÷LB(b).
A rounded value has a range
A value given to a degree of accuracy could really be anything in a range half a unit either side of it.
Drawn from real examiner reports.
Substituting rounded values, not bounds
Putting the given (rounded) numbers into the formula and then "finding bounds" of the result scores nothing.
A commonly reported examiner note records.
Mixing upper and lower bounds in one formula
Substituting a mixture (e.g. an upper bound for one quantity and the rounded value for another) loses marks.
A commonly reported examiner note records.
Upper bound 28.5, not 28.499…
The upper bound is the exact halfway value (28.5), not a string of 9s like 28.499 — terminating decimals just below it are not accepted.
A commonly reported examiner note records.
Wrong half-unit for the accuracy
The interval is half of the rounding unit, not always . To d.p. it is ; to the nearest it is . So to d.p. has upper bound , not .
Wrong bounds for a subtraction
For a maximum difference use : subtracting the smallest possible makes the result largest. Using (or both lower) gives the wrong extreme.
Give the answer to the accuracy asked
If asked for an answer to 3 s.f., round at the end — don't leave 12.750… unrounded.
Write each error interval separately
When quantities are rounded to different accuracies, write the error interval for each one at its own accuracy first, then pick the right end of each for the bound you want. Do not assume for everything.
Quote accuracy both bounds agree on
If the upper and lower bounds of a result round to the same value (e.g. and both give to 2 s.f.), that shared value is a suitable degree of accuracy to state for the answer.
A measurement rounded to the nearest lies within of the stated value:
12 cm to the nearest cm — bounds?
A length cm, measured to the nearest centimetre. Write down the lower and upper bounds of .
