Question

if the actual value of a physical quantity is 1.0and its measured value is 1.05,calculate absolute value,relative error and percentage error

Answer 1

Answer:

• Measured value of a physical quantity = 1.05
• Actual value of a physical quantity = 1.0
• Absolute error = ?
• Relative error = ?
• Percentage error = ?

Absolute Error:

$\implies \sf \Delta x = x_{(measured\:value)} - x_{(Actual\:value)}$

$\implies \sf \Delta x = 1.05 - 1.0$

$\implies \sf \boxed{ \bf \Delta x = 0.05 }$

Relative Error:

$\implies \sf Relative \: Error = \dfrac{\Delta x}{x_{(Actual\:value)}}$

$\implies \sf Relative \: Error = \dfrac{0.05}{1.0}$

$\implies \boxed{ \bf Relative \: Error = 0.05}$

Percentage Error:

$\implies \sf \% \: Error = \dfrac{\Delta x}{x_{(Actual\:value)}} \times 100$

$\implies \sf\% \: Error = \dfrac{0.05}{1.0} \times 100$

$\implies \boxed{\bf\% \: Error = 5 \: \%}$

Answer 2

★ Given :-

• Actual Value = 1.0
• Measured Value = 1.05

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★ To Find :-

• Absolute Error = ?
• Relative Error = ?
• Percentage Error = ?

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★ Solution :-

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∓ Here, it is given that, Actual Value of the physical quantity is 1.0 , Measured Value of the physical quantity is 1.05 . And, we have to find the value of Absolute Error , Relative Error & Percentage Error .

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• Now, let's solve step by step -----

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◆ First, we will calculate the Absolute Error :-

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$\small\bull \: \sf{Absolute \: Error=Measured \: Value - Actual \: Value } \\ \\ \small\sf{Absolute \: Error = 1.05 - 1.0} \\ \\ \small\sf{Absolute \: Error = 0.05}$

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◆ Now, we will calculate the Relative Error :-

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$\small\bull \: \sf{Relative \: Error = \frac{Absolute \: Error}{Actual \: Value} } \\ \\ \small\sf{Relative \: Error = \frac{0.05}{1.0} } \\ \\ \small\sf{Relative \: Error = 0.05}$

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◆ Here, we will calculate the Percentage Error :-

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$\small\bull \: \sf{Percentage \: Error = \frac{Absolute \: Error}{Actual \: Value} \times 100 } \\ \\ \small\sf{Percentage \: Error = \frac{0.05}{1.0} \times 100 } \\ \\ \small\sf{Percentage \: Error =5 \% }$

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★ Hence :-

• Absolute Error = 0.05
• Relative Error = 0.05
• Percentage Error = 5%

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