The upper bound for a rounded number is the smallest value that would round up to the next rounded value.

The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.

An error interval for a number x shows the range of possible values of x.  It is written as an inequality a ≤ x < b

Upper and lower bounds in additive calculations

Maths

Upper and lower bounds

Upper and lower bounds in multiplicative calculations

Using upper and lower bounds practically

Advanced problem solving with rounding, estimation and bounds

In the prior unit, pupils learnt how to round to a given number of decimal places or significant figures and explored the effect of using rounded numbers for calculations. In this unit, pupils will investigate the bounds and perform calculations to determine a best/worst case scenario.

This unit explores the impact of upper and lower bounds on additive and multiplicative calculations.

Rounding, estimation and bounds

The numbers either end of an error interval are called the lower and upper {{ }}.

A piece of string is measured as 10.2 cm correct to 1 decimal place.  What are the lower and upper bounds?

A piece of string is measured as 10.2 cm correct to 1 decimal place.  The lower and upper bounds are 10.15 and 10.25.  What is the error interval?

The mass of a cat is 4.8 kg correct to 2 significant figures.  What is the error interval?

Here are the error intervals for $$x$$ and $$y$$:  $$24.5\leq{x}<25.5$$ and $$9.5\leq{y}<10.5$$.  What are the lower and upper bounds of $$x + y$$?

Here are the error intervals for $$x$$ and $$y$$:  $$24.5\leq{x}<25.5$$ and $$9.5\leq{y}<10.5$$.  What are the lower and upper bounds of $$x - y$$?

An error interval for a number shows the {{ }} of possible values of the number.

Work out the lower and upper bounds of 560 rounded to the nearest 10

Work out the lower and upper bounds of 4.8 rounded to 1 decimal place.

{{ }} rounded to the nearest integer.  The lower bound is 8.5 and the upper bound is 9.5

{{ }} rounded to 1 decimal place.  The lower bound is 1.65 and the upper bound is 1.75

{{ }} rounded to 2 significant figures.  The lower bound is 1250 and the upper bound is 1350

Upper and lower bounds in additive calculations

Lesson outcome