The Pentagon wants to train about 135,000 police officers, 62,000 national guardsmen, 24,000 army troops and others for a security force totaling 271,041.

What is extraordinary is this number: 271,041. Not, mind you, “271,042″ or “271,043″ or even “about 270,00″, but exactly “271,041″. [N.B. This statement originated with The Pentagon, and not with the LA Times.]
This is a beautiful example of gratuitous quantification and misguided precision. In this context, specifying “…and forty-one” is simply absurd: there is no reason to think that the number could possibly be known to that precision, and suggesting otherwise is misleading , inaccurate, and wrong, as well as being an obvious display of innumeracy that should never appear in Congressional testimony or come out of the Pentagon.
All this would be true, even if the first part of the statement didn’t say

The Pentagon wants to train about 135,000 ….

thus limiting, by saying “about”, the expected precision of the numbers right up front.