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Math Help - 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 64.5 litres and 65.5 litres. The maximum error is therefore 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
    \frac{0.5}{65}\times 100%
    =0.77%, correct to 2 d.p.
    and then subtract this from 100% to give the degree of accuracy. 100 - 0.77 = 99.23. So the figure is 99.23% accurate.

    Grandad
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