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Error intervals
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EasyQuestion 1
[2 marks]A length is measured as 8 cm, correct to the nearest centimetre.
Write down the error interval for the length.
Solution for Question 1
MediumQuestion 2
[3 marks]A number x is rounded to 2 decimal places.
The result is 3.47.
(a) Write down the error interval for x.
(b) What is the largest possible value of x?
Solution for Question 2
HardQuestion 3
[4 marks]A rectangle has length 12.4 cm and width 5.8 cm, both measured correct to 1 decimal place.
Calculate the lower bound and upper bound for the perimeter of the rectangle.
Solution for Question 3
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When a number is rounded, we lose precision. Error intervals show the range of possible original values. If 35 is the result of rounding to the nearest integer, the original could be anywhere from 34.5 (inclusive) up to 35.5 (exclusive).
We write this as: 34.5 ≤ x < 35.5. Note the inclusive lower bound (≤) and exclusive upper bound (<). The lower bound rounds up to 35, and anything from 35.5 would round up to 36.
For different levels of rounding, adjust the bounds accordingly. If 3.5 is rounded to 1 decimal place, the error interval is 3.45 ≤ x < 3.55. If 400 is rounded to the nearest 100, the error interval is 350 ≤ x < 450.
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