AQA · Mathematics · 8300
GCSE Maths: Error Intervals
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Error Intervals (Corbettmaths Video 377), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the error interval for a mass of 58 g measured to the nearest gram?
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57.5 g ≤ mass < 58.5 g
What is the error interval for a distance of 300 miles given to the nearest 100 miles?
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250 miles ≤ distance < 350 miles
What is the error interval for a number p rounded to 2 decimal places as 10.68?
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10.675 ≤ p < 10.685
What is the error interval for a number x rounded to 3 significant figures as 12.7?
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12.65 ≤ x < 12.75
A rectangle measures 20 cm by 6 cm, each to the nearest cm. What is the error interval for its area A?
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107.25 cm² ≤ A < 133.25 cm² (from 19.5 × 5.5 and 20.5 × 6.5).
Why can a total of 8 min 58 s be valid for two songs given as 3 min and 5 min to the nearest minute?
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The total time T satisfies 7 min ≤ T < 9 min, so any value up to (but not including) 9 min is possible.
What is the error interval for a length L truncated to 1 decimal place as 2.6 cm?
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2.6 cm ≤ L < 2.7 cm
How does the error interval for a truncated value differ from a rounded one?
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A truncated value is the lower bound itself; the upper bound is one unit of the truncation place higher (e.g. 39.1 truncated to 1 d.p. gives 39.1 ≤ n < 39.2).
If x is truncated to 8.25 (first three calculator digits), the error interval is 8.25 ≤ x < ?.
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8.26
Why is rounding a calculator answer preferable to truncating it?
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The true value may be very close to the next digit (e.g. 8.2599), so truncating to 8.25 is less accurate than rounding to 8.26.
A regular pentagon has perimeter 18 cm to the nearest cm. What is the error interval for the side length x?
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3.5 cm ≤ x < 3.7 cm (from 17.5 ÷ 5 and 18.5 ÷ 5).
How do you find the upper bound of a speed from a distance and a time given to the nearest 10 units?
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Divide the upper bound of the distance by the lower bound of the time (e.g. 405 m ÷ 75 s = 5.4 m/s).
What is the error interval for a number y that is 100 when rounded to 1 significant figure?
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50 ≤ y < 150
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