Bounds and Error Intervals [H]

This lesson covers bounds and error intervals for AQA GCSE Mathematics Higher Tier. When a measurement is rounded, the true value could lie anywhere within a range. Understanding this range — defined by upper and lower bounds — is essential for questions on accuracy and for using bounds in calculations.

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What Are Bounds?

When a value has been rounded or truncated, the actual value lies within a range. The limits of this range are called bounds.

• The lower bound (LB) is the smallest value that would round to the given number.
• The upper bound (UB) is the smallest value that would round up to the next number.

Key Principle

If a measurement is given as x, rounded to a certain degree of accuracy, then the true value v satisfies:

Lower Bound <= v < Upper Bound

Note: the lower bound is included (<=) but the upper bound is excluded (<).

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Finding Bounds for Rounded Values

The bounds depend on the degree of accuracy used in the rounding.

The Rule

Lower bound = rounded value - half the degree of accuracy