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

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

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

Advanced problem solving with rounding, estimation and bounds

Maths

Upper and lower bounds

Upper and lower bounds in additive calculations

Upper and lower bounds in multiplicative calculations

Using upper and lower bounds practically

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

An error {{ }} for a number $$x$$ shows the range of possible values of $$x$$. 

Using estimation only which of the following is the correct answer to $${{214^2\times2.875}\over37.06}$$

Estimate the value of $${{19.56^3}\over{37.06-16.2}}$$

Which of the following calculations will give the lower bound of $$a^2$$?

If $$LB_x = 0.4562$$ and $$UB_x = 0.4569$$.  Find the value of $$x$$ and the appropriate degree of accuracy in significant figures.

$$a$$ = 2.64 (3 s.f.), $$b$$ = 1.655 (4 s.f.), $$c={\sqrt{a}\over{b^3}}$$.  Work out the value of $$c$$ to a suitable degree of accuracy.

A quick estimate for a calculation is obtained from using approximate values, often rounded to {{ }} significant figure. 

A piece of string is measured as 6.8 cm correct to 1 decimal place.  What are the lower and upper bounds?

$${A} = {1\over2}\times{{(a+b)\times{h}}}$$

Which of the following is not a correct formula for the area of a trapezium? [IMG]

Which calculation will give the upper bound of $$a\times{b}$$?

Which calculation will give the lower bound of $$a\div{b}$$?

Starter Quiz

A quick estimate for a calculation is obtained from using approximate values, often rounded to significant figure.