Upper And Lower Bounds - GCSE Maths - Third Space Learning

Home » How To Find Upper And Lower Bounds » Upper And Lower Bounds - GCSE Maths - Third Space Learning

Maybe your like

What are upper and lower bounds?

Upper and lower bounds are the maximum and minimum values a number could have been before it was rounded.

The lower bound is the smallest value that would round up to the estimated value. The upper bound is the smallest value that would round up to the next estimated value.

They can also be called limits of accuracy. The upper and lower bounds can be written using error intervals.

For example, A rectangle has a width of 4.3 cm rounded to 1 decimal place and a length of 6.4 cm rounded to 1 decimal place.

Let’s look at the length:The smallest number that will round up to give 6.4 is 6.35, this is the lower bound. The largest number that will round down to give 6.4 is 6.44999… so we say that 6.45 is the upper bound.

Therefore we can write:

\[ 6.35 \mathrm{~cm} \leq l<6.45 \mathrm{~cm} \]

Let’s look at the width:The smallest number that will round up to 4.3 is 4.25, this is the lower bound. The largest number that will round down to give 4.3 is 4.34999… so we say that 4.35 is the upper bound.

Therefore we can write:

\[ 4.25 \mathrm{~cm} \leq w<4.35 \mathrm{~cm} \]

We use ≤ for the lower bound as 4.25 would round up to 4.3 but we have to use < for the upper bound as 4.35 would round up to 4.4, not down to 4.3.

These upper and lower bounds of the length and width can then be used to find the upper and lower bounds of the perimeter and area of the rectangle.

Step-by-step guide: Error intervals

See also: Rounding numbers

What are upper and lower bounds?

What are upper and lower bounds?

Tag » How To Find Upper And Lower Bounds