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 multiplicative calculations

Maths

Upper and lower bounds

Upper and lower bounds in additive 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 lower bound for a rounded number is the {{ }} value the number could have taken prior to rounding.

$$x$$ = 4.5 correct to 1 decimal place.  What is the error interval?

$$y$$ = 26 correct to 2 significant figures.    What is the error interval?

The error interval of $$x$$ is $$4.45\leq{x}<4.55$$.  The error interval of $$y$$ is $$25.5\leq{y}<26.5$$.  What are the lower and upper bounds of $$xy$$?  (Give you answers to 3 decimal places)

The error interval of $$x$$ is $$4.45\leq{x}<4.55$$.  The error interval of $$y$$ is $$25.5\leq{y}<26.5$$.  What are the lower and upper bounds of $$x\over{y}$$? (Give you answers to 3 s.f.)

Which calculation will give the lower bound of $$x={{a+b}\over{c}}$$?

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

The length of a leaf is measured as 6.7 cm correct to 1 decimal place.  What are the lower and upper bounds?

The length of a leaf is measured as 6.7 cm correct to 1 decimal place.  The lower and upper bounds are 6.65 and 6.75.  What is the error interval?

The mass of a kitten is 1.3 kg correct to 2 significant figures.  What is the error interval?

Here are the error intervals for $$x$$ and $$y$$:  $$12.5\leq{x}<13.5$$ and $$3.5\leq{y}<4.5$$.  What are the lower and upper bounds of $$x + y$$?

Here are the error intervals for $$x$$ and $$y$$:  $$12.5\leq{x}<13.5$$ and $$3.5\leq{y}<4.5$$.  What are the lower and upper bounds of $$x - y$$?

Upper and lower bounds in multiplicative calculations

Lesson outcome