Bounds | CIE IGCSE Maths: Core Revision Notes 2023

Bounds & Error Intervals

Bounds are the smallest (lower bound, LB) and largest (upper bound, UB) numbers that a rounded number can lie between
- It simply means how low or high the number could have been before it was rounded
The bounds for a number, $x$ , can be written as $LB \leq x < UB$
- Note that the lower bound is included in the range of values $x$ could have taken but the upper bound is not

The basic rule is “Half Up, Half Down”
- UPPER BOUND – To find the upper bound add on half the degree of accuracy
- LOWER BOUND – To find the lower bound take off half the degree of accuracy
- ERROR INTERVAL: LB ≤ x < UB
Note that it is tempting to think that the Upper Bound should end in a 9, or 99, etc. but if you look at the Error Interval – LB ≤ x < UB – it does NOT INCLUDE the Upper Bound so all is well
- the upper bound is the cut off point for the greatest value that the number could have been rounded from but will not actually round to the number itself

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

Find the lower and upper bounds for $l .$

The degree of accuracy is 1 decimal place, or 0.1 km so the true value could be up to 0.05 km above or below this

Upper bound:

3.6 + 0.05 = 3.65 km

Lower bound:

3.6 - 0.05 = 3.55 km

Upper bound: 3.65 km
Lower bound: 3.55 km

We could also write this as an error interval of $3.55 \leq l < 3.65$ , although this is not asked for in this question