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Thread: Relative Error & Maximum Error

  1. #1
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    Red face 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?
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  2. #2
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    Hello sallyjs

    Welcome to Math Help Forum!
    Quote Originally Posted by sallyjs View Post
    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.

    Grandad
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