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

Maths

Upper and lower bounds in additive calculations

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

Upper and lower bounds are used when a number has been {{ }}.

Work out the lower and upper bounds of 320 rounded to the nearest 10

Work out the lower and upper bounds of 12.6 rounded to 1 decimal place.

{{ }} rounded to the nearest integer.  The lower bound is 147.5 and the upper bound is 148.5

{{ }} rounded to 1 decimal place.  The lower bound is 10.25 and the upper bound is 10.35

{{ }} rounded to 2 significant figures.  The lower bound is 8750 and the upper bound is 8850

In the number 56 392 the 3 is the third {{ }} figure.

Choose the correct calculation to estimate the cost of hiring an electrician for 4.5 hours, where the total cost = £42.50 × number of hours + £25 

Estimate the value of $${435.8\times8.742\over3.04}$$

Will the estimation of 128.03 + 0.512 be an overestimate or underestimate?

Estimate the amount of change received from £500 when purchasing a TV costing £375

Estimate the circumference of a circle with a radius of 8.4 cm.

Upper and lower bounds

Lesson outcome