Advanced problem solving with rounding, estimation and bounds | Maths

Starter quiz

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

'1' ✓
Round 508 273 to 2 significant figures.

'510 000' ✓
A piece of string is measured as 6.8 cm correct to 1 decimal place. What are the lower and upper bounds?

'6.75 cm and 6.85 cm' ✓
Which of the following is not a correct formula for the area of a trapezium? [IMG]

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

${A} = {{a+bh}\over2}$ ✓

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

${A} = {1\over2}\times{{(a+b)\times{h}}}$
Which calculation will give the upper bound of $a\times{b}$ ?

$LB_a\times{LB_b}$

$LB_a\times{UB_b}$

$UB_a\times{UB_b}$ ✓

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

$LB_a\div{UB_b}$ ✓

$LB_a\div{LB_b}$

$UB_a\div{UB_b}$

$UB_a\div{LB_b}$

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

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

355.2711819

3552.711819 ✓

35527.11819

355271.1819

3552711.819
Estimate the value of ${{19.56^3}\over{37.06-16.2}}$

'400' ✓
Which of the following calculations will give the lower bound of $a^2$ ?

$a^2=UB_{c^2}-UB_{b^2}$

$a^2=LB_{c^2}-LB_{b^2}$

$a^2=LB_{c^2}-UB_{b^2}$ ✓

$a^2=UB_{c^2}-LB_{b^2}$
If $LB_x = 0.4562$ and $UB_x = 0.4569$ . Find the value of $x$ and the appropriate degree of accuracy in significant figures.

$x$ = 0.45 (2 s.f.)

$x$ = 0.45 (3 s.f.)

$x$ = 0.46 (2 s.f.) ✓

$x$ = 0.46 (3 s.f.)

$x$ = 0.456 (3 s.f.)
$a$ = 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.

$x$ = 0.35 (2 s.f.)

$x$ = 0.35 (3 s.f.)

$x$ = 0.36 (3 s.f.)

$x$ = 0.36 (2 s.f.) ✓

$x$ = 0.358 (3 s.f.)

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Rounding and estimation are practical maths skills.
Sometimes you will need to apply common sense to rounding in context.
Using your knowledge of arithmetic procedures, you can determine which bounds to calculate with.

Truncating the numbers rather than rounding when considering the suitable degree of accuracy.

Emphasise that the numbers are being rounded and therefore the digit in the next decimal place must be considered.

Lower bound - The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded
Upper bound - The upper bound for a rounded number is the smallest value that would round up to the next rounded value
Error interval - An error interval for a number x shows the range of possible values of x. It is written as an inequality a ≤ x < b