Question

A rock weighs 2.467kg and student measured it's weight on a scale as 2.45kg calculate: a) absolute error b)relative error c) percentage error

Answer 1

Given:

A rock weighs 2.467 kg and student measured its weight on a scale of 2.45 kg

To find:

Absolute error

Relative error

Percentage error

Solution:

The actual value = 2.467 kg

The measured value = 2.45 kg

Finding the absolute error:

We know,

$\bigstar\boxed{\bold{Absolute\:Error = Actual \:value - Measured\: value}}\bigstar$

∴ The absolute error is,

= 2.467 kg - 2.45 kg

= 0.017 kg

Thus, the absolute error is → $\boxed{\bold{\underline{0.017\:kg}}}$.

Finding the relative error:

We know,

$\bigstar\boxed{\bold{ Relative \:Error= \frac{Absolute\:Error}{Actual \:value} }}\bigstar$

∴ The relative error is,

= $\frac{0.017\:kg}{2.467\:kg}$

= 0.00689

≈ 0.0069

Thus, the relative error is → $\boxed{\bold{\underline{0.0069}}}$.

Finding the percentage error:

We know,

$\bigstar\boxed{\bold{ Percentage \:Error= Relative\:Error\times 100\% }}\bigstar$

∴ The percentage error is,

= 0.0069 × 100%

= 0.69%

Thus, the percentage error is → $\boxed{\bold{\underline{0.069\%}}}$.

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