Scien­tists should acknowl­edge the lim­i­ta­tions of their method and the lim­i­ta­tions of the results they are pre­sent­ing up front and not wait for the defense to develop the con­cept (if they even know to do so).

What should attor­neys know about sig­nif­i­cant dig­its or figures?

It is all about super­flu­ous pre­ci­sion.  To a non-technical per­son, a mea­sure­ment seems to be really pow­er­ful if it has a lot of dig­its after the zero.

Think about this example…

Foren­sic sci­ence can be inap­pro­pri­ately used and result in mis­lead­ing measurements

Wow the green object is 4.81950 inches!  Sounds really pre­cise and exact­ing, doesn’t it?  But the truth is that due to the uneven­ness of the object and the coarse­ness of the ruler, the best we can say is the length is about 4.8 inches.  Report­ing any­thing other than this about 4.8 inches (ignor­ing for the moment the large and impor­tant con­cept of uncer­tainty bud­get­ing) is mis­lead­ing as it implies the mea­sure­ment is pre­cise and exact to 5 dec­i­mal places.

This is where the con­cept of “sig­nif­i­cant fig­ures” come into play.

For exam­ple, the pop­u­la­tion of a city might only be known to the near­est thou­sand and be stated as 42,000, while the pop­u­la­tion of a coun­try might only be known to the near­est mil­lion and be stated as 42,000,000. The for­mer might be in error by hun­dreds, and the lat­ter might be in error by hun­dreds of thou­sands, but both have two sig­nif­i­cant fig­ures (4 and 2). This reflects the fact that the sig­nif­i­cance of the error (its likely size rel­a­tive to the size of the quan­tity being mea­sured) is the same in both cases.

Well how does this typ­i­cally happen?

Exam­ple of Spu­ri­ous figures

Spu­ri­ous dig­its intro­duced, for exam­ple, by cal­cu­la­tions car­ried out to greater accu­racy than that of the orig­i­nal data, or mea­sure­ments reported to a greater pre­ci­sion than the equip­ment supports.

The source of the mea­sure­ment is crucial

Think about this in the sense of acci­dent scene recon­struc­tion where speed is the cru­cial mea­sure­ment sought to be dis­cov­ered and cal­cu­lated.  This is often derived from length mea­sures.  This is where your mea­sure­ment device and its sig­nif­i­cant dig­its can be cru­cial.  It can lead to erro­neous answers otherwise.

Mea­sure­ment can be key in the pre­ci­sion and accu­racy of a result

The Two Great­est Sources of Error Regard­ing Sig­nif­i­cant Dig­its

1. Writ­ing more dig­its in an answer (inter­me­di­ate or final) than jus­ti­fied by the num­ber of dig­its in the data.
2. Rounding-off, say, to two dig­its in an inter­me­di­ate answer, and then writ­ing three dig­its in the final answer.

We can­not ignore sig­nif­i­cant digits.