A student weighed a 26.91 g block to the nearest 0.01 g and measured its volume

Question

A student weighed a 26.91 g block to the nearest 0.01 g and measured its volume as 25 ml to the nearest ml. What is the uncertainty in the calculated density? Density = 26.91 g plusminus 0.01 g/25 ml plusminus 1 ml = 1.0764 g/ml The density is 1.0764 g/ml. It should not be rounded off yet! Do you know why? Find % uncertainty in mass. Find % uncertainty in volume. Find % uncertainty in density. Find absolute uncertainty in density. Now report the density to the correct number of significant figures? Report the answer in the correct number of significant figures. Why did you round off the density to the hundredth place? Notice that the answer 1.08 g/ml has three significant figures although the denominator in the density set up (25 ml) has only two significant figures. Consider the following operation: 1.85 g(plusminus 0.02 g)/0.48 cm(plusminus 0.02 cm) times l.67 cm(plusminus 0.03 cm) = Follow the steps given below to find how the answer should be rounded off. Give the answer without rounding off. Find % uncertainty in the reading, 1.85 g. Find % uncertainty in the reading, 0.48 cm.

Explanation / Answer

Exercise 1-

Weight = 26.91g +/- 0.01 g (given)

Volume = 25ml +/- 1ml

D = M/V = 26.91g +/- 0.01 g/25ml +/- 1ml = 1.0764g/l

Density should be not rounded off yet, because uncertainty in density is not calculated at this time.

a.

Weight = 26.91g +/- 0.01 g (given)

Percentage uncertainty = (uncertainty in weight/ value for weight)* 100%

Percentage uncertainty = (0.01 g /26.91g)* 100%

= 0.0003*100% = 0.03%

b.

Volume 25ml +/- 1ml

Percentage uncertainty = (uncertainty in volume/ volume)* 100%

Percentage uncertainty = (1ml /25)* 100%

                                           = 4%

c.

% uncertainty in density –

Density = mass /volume

              = (26.91g +/- 0.01 g) /(25ml +/- 1ml)

              = 1.0764g/l +/- 4%

d. absolute uncertainty in density-

1.0764g/l x 4/100 = 0.04g/l

e. The density (with the correct number of significant figures is) = 1.08 g/l

f. . Finally, the density (with the correct number of significant figures is) = 1.08 +/- 0.04 g/l

g.We rounded off the density to hundredth place, because uncertainty in density is +/- 0.04 g/l

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