Question

If the weight of an unknwon sample is greater than 1g, as it may be with pottassium phthalate samples of low percentage purity, why does this sample need only to be weighed to the nearest milligram?

Answer 1

This is because to have negligible percentage error this precision/accuracy is sufficient.

The percentaage error becomes negligible even when we weigh to the nearest milligram (that is upto the third decimal) It is not necessary to weigh upto the fourth decimal because it wil not affect the accuracy of the measurement to any great extent

ILLUSTRATION:

Case 1:

Suppose 1.001 g is weighed as 1.000 g (nearest milligram)

Error = 1.001 -1.000 = 0.001 g

Percentage error = 0.001 x100/1 = 0.1% which is negligible

This percentage error is acceptable in the case of samples of low percentage purity

Even if you weigh 1.009 g as 1.000 g , the error (0.9%) will be still less than 1% and acceptable

Case 2:

Suppose 1.0001 g is weighed as 1.0000 g (upto the fourth decimal)

Error = 1.0001 -1.0000 = 0.0001 g

Percentage error = 0.0001 x100/1 = 0.01% which is negligible .

Such low percentage error is not required in the case of samples of low percentage purity

Case 3:

Suppose 1.01 g is weighed as 1.00 g

Error = 1.01 -1.00 = 0.01 g

Percentage error = 0.01 x100/1 =1 % This error is considerable