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## Homework Statement

The density of the material of a rectangular block is determined by measuring the mass and linear dimensions of the block. The table shows the results obtained, together with their uncertainties.

Mass [tex]= (25.0 \pm 0.1)g[/tex]

Lenght [tex]= (5.00 \pm 0.01)cm[/tex]

Breath [tex]= (2.00 \pm 0.01)cm[/tex]

Height [tex]= (1.00 \pm 0.01)cm[/tex]

The density is calculated to be [tex]2.50gcm^-3[/tex]

What is the uncertainty in this result?

## Homework Equations

Density = Mass / Volume

Percentage Uncertainty = Acutal Uncertainty / True Value * 100

## The Attempt at a Solution

Mass % Uncertainty [tex]= \frac{0.1}{25.0} \times 100 = 0.4\%[/tex]

Lenght % Uncertainty [tex]= \frac{0.01}{5.00} \times 100 = 0.2\%[/tex]

Breath % Uncertainty [tex]= \frac{0.01}{2.00} \times 100 = 0.5\%[/tex]

Height % Uncertainty [tex]= \frac{0.01}{1.00} \times 100 = 1\%[/tex]

Density % Uncertainty = [tex]\frac{Mass \% Uncertainty}{Volume \% Uncertainty} = \frac{0.4}{0.2+0.5+1} = 0.5\%[/tex]

Absoulte Value = [tex]\frac{0.5 \times 2.50}{100} = 0.0125gcm^-3[/tex]

Density = [tex]2.50 \pm 0.0125 gcm^-3[/tex]

Is this right?

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