GCSEMaths: FoundationEdexcelRevision NotesNumberRounding, Estimation & Error IntervalsError Intervals

Error Intervals (Edexcel GCSE Maths: Foundation)

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Naomi C

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Naomi C

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Error Intervals

What is an error interval?

  • An error interval is the range of possibles values that a number could have been before it was rounded or truncated

How do we find the error interval for a rounded number?

  • Think about the smallest and biggest numbers that a value could be before they round up to the next value or down to the previous value
  • You may be given a question where the number has been rounded to a given degree of accuracy
    • E.g. A stick has a length, l, of 5 cm correct to the nearest whole number
      • It could have been as short as 4.5 cm and still been rounded up to 5 cm
      • It could have been up to (but not including) 5.5 cm before it was rounded down to 5 cm
      • The error interval for the length of the stick is 4.5 less or equal than l less than 5.5
  • The rounded value should be the midpoint of the error interval

How do we find the error interval for a truncated number?

  • You may be given a question where the number has been truncated
    • E.g. The first 3 digits of an answer, a, to a calculation have been written down as 2.95
      • The smallest value that the answer could have been is 2.95
      • The largest value that the number could have been up to (but not equal to) is 2.96 before it was truncated to 2.95
      • The error interval for the size of the number is 2.95 less or equal than a less than 2.96
  • The truncated value should be the same as the smallest value in the error interval

Exam Tip

  • Read the exam question carefully to correctly identify the degree of accuracy.
    •  It may be given as a place value, e.g. rounded to 1 s.f., or it may be given as a measure, e.g. nearest metre or it may have been truncated.

Worked example

The length of a road, l km, is given as l equals 3.6, correct to 1 decimal place.

Write down the error interval for l.

The degree of accuracy is 1 decimal place, or 0.1 km
The previous 0.1 km value is 3.5 km
The shortest length that the road could have been and still been rounded up to 3.6 km (instead of 3.5 km) is 

Shortest possible length = 3.55 km

The next 0.1 km value is 3.7 km
The greatest possible length that the road could have been and still be rounded down to 3.6 km (instead of 3.7 km) is

Longest possible length < 3.65 km

Write down the error interval using inequality notation

 bold 3 bold. bold 55 bold space bold less or equal than bold space bold italic l bold space bold less than bold space bold 3 bold. bold 65

Worked example

The mass of a dog, m kg, is given as m equals 14, truncated to 2 significant figures.

Write down the error interval for m.

The degree of accuracy is 2 significant figures, which is 1 kg in this question
A mass of 13.999 kg would be truncated to 13 kg
The smallest possible mass would be 14 kg itself

Smallest possible mass = 14 kg

14.999 kg would be truncated to 14 kg
15 kg would be truncated to 15 kg
The largest possible mass is therefore 15 kg but it can not be equal to this value

Largest possible mass < 15 kg

Write down the error interval using inequality notation

 bold 14 bold space bold less or equal than bold space bold italic m bold space bold less than bold space bold 15

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    Naomi C

    Author: Naomi C

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.