# Relative Error & Maximum Error

• Mar 8th 2010, 11:39 PM
sallyjs
Relative Error & Maximum Error
A car's fuel tank has a capacity of 65 litres. If this capacity is given to the nearest litre, find the degree of accuracy correct to 2 decimal places.

First step is finding the maximum error. What is maximum error, and how do I find it?
• Mar 10th 2010, 01:40 AM
Hello sallyjs

Welcome to Math Help Forum!
Quote:

Originally Posted by sallyjs
A car's fuel tank has a capacity of 65 litres. If this capacity is given to the nearest litre, find the degree of accuracy correct to 2 decimal places.

First step is finding the maximum error. What is maximum error, and how do I find it?

If the capacity is given to the nearest litre, then this means that the true capacity lies anywhere between $\displaystyle 64.5$ litres and $\displaystyle 65.5$ litres. The maximum error is therefore $\displaystyle 0.5$ litre.

I'm not certain how the degree of accuracy is to be expressed, but a percentage would be quite a sensible way. So we need first to express the maximum error as a percentage of the stated capacity - that's
$\displaystyle \frac{0.5}{65}\times 100$%
$\displaystyle =0.77$%, correct to 2 d.p.
and then subtract this from $\displaystyle 100$% to give the degree of accuracy. $\displaystyle 100 - 0.77 = 99.23$. So the figure is $\displaystyle 99.23$% accurate.