- A time is 12.4 seconds, correct to 1 decimal place. Write down the error interval for the time .[2]
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A recipe says 250 g of flour, measured to the nearest 10 g. The flour could weigh anything from 245 g up to just under 255 g. Writing that range as an , and working out how rounding affects the result of a calculation, is what this lesson is about.
The big picture
Rounding replaces a whole range of possible values with a single number. The and mark the edges of that range: half a unit below and half a unit above the rounded value. The lower bound is included; the upper bound is not, because it would round up.
At Higher tier, AQA asks for bounds of calculations — the greatest possible speed, the smallest possible area — and for answers "to an appropriate degree of accuracy". The trick is to think about each input separately: which bound makes the answer as large, or as small, as possible?
What you'll learn
Find the unit the value was rounded to, halve it, and go that far either side.
A length of 8.4 cm to 1 decimal place was rounded to the nearest 0.1 cm, so half a unit is 0.05 cm: .
A crowd of 3000 to the nearest 100 people: .
A length is 7.4 cm, correct to 1 decimal place. Write down its lower bound.
Tip — Write the interval with on the left and on the right. Using at both ends is the most common way to lose this mark.
Truncating chops off digits without rounding. A calculator display of 6.27 truncated to 1 decimal place gives 6.2.
So if after truncation to 1 d.p., the true value could be anything from 6.2 up to, but not including, 6.3: .
Rounding spreads the interval evenly around the value; truncation puts it entirely above. That difference is why AQA always tells you which one was used.
Adding or multiplying: use both upper bounds for the maximum and both lower bounds for the minimum.
Subtracting : maximum uses upper and lower .
Dividing : maximum uses upper and ; minimum uses lower and upper .
A rectangle measures 8 cm by 5 cm, both to the nearest cm. Work out the upper bound of its area, in cm².
Tip — Dividing by a smaller number gives a bigger answer. That is why the lower bound of the denominator gives the upper bound of the result.
Round the upper and lower bounds to the same accuracy. The most accurate rounding where they agree is the appropriate answer.
For the density above, 6.14 and 5.76 do not agree to 1 decimal place (6.1 and 5.8), but both round to 6 to 1 significant figure.
Think like an examiner
Remember these
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Stretch yourself
A sprinter runs 100 m, measured to the nearest metre, in 12.3 seconds, measured to the nearest 0.1 s. Calculate the upper and lower bounds of her average speed, and give the speed to a suitable degree of accuracy.
Hint — Maximum speed: longest distance in the shortest time.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 8 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
A runner covers 100 m, correct to the nearest metre, in 12.3 seconds, correct to 1 decimal place.
and , both correct to 1 decimal place.
Unlimited practice
A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.
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Test yourself
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Real past-paper questions on Error Intervals & Bounds, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.