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A bottle of mineral water has a capacity of 500 ± 0.5 millilitres. Find the (a) tolerance, (b) percentage error. The diagram shows a circle centre O with six identical triangles shaded.

Mathematics

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Here's the solution for the first question:

Given the capacity of a bottle of mineral water is 500±0.5500 \pm 0.5 millilitres.

Part a· 1 step

Find the tolerance.

  1. Identify the tolerance from the given capacity.

    The tolerance is the maximum allowable deviation from the specified value. In the expression 500±0.5500 \pm 0.5 millilitres, the tolerance is the ±\pm value.
    The tolerance is 0.5 millilitres.

    Tolerance=0.5 ml\text{Tolerance} = \boxed{\text{0.5 ml}}

Part b· 2 steps

Find the percentage error.

  1. Identify the absolute error and the nominal value.

    The absolute error is the tolerance, which is 0.5 ml.
    The nominal (or measured) value is 500 ml.

  2. Calculate the percentage error using the formula

    Percentage Error=Absolute ErrorNominal Value×100%\text{Percentage Error} = \frac{\text{Absolute Error}}{\text{Nominal Value}} \times 100\% Percentage Error=0.5500×100%\text{Percentage Error} = \frac{0.5}{500} \times 100\% Percentage Error=0.001×100%\text{Percentage Error} = 0.001 \times 100\% Percentage Error=0.1%\text{Percentage Error} = 0.1\%

    The percentage error is 0.1%\boxed{\text{0.1\%}}.

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