Here is a great example I used to give engineering students who insisted on copying down 14 significant digit answers (directly from their calculators) about why significant digits keep you from looking stupid.
A docent shows a class of kindergartners a T-Rex skeleton. Little Johnny asks "Mister, how old is this skeleton?"
The docent replies: "This skeleton is 65 million and 20 years plus 14 days and 3 hours old."
"Wow!" says the kid, "How do they date it so accurately?"
The docent replies: "Because I just had my 20th anniversary two weeks ago on Monday, and we are a hour away from lunch, and on the day I was hired they told me that this skeleton was 65 million years old!"
Here's another example: The liars at NASA claim that 2014 was "the warmest year on record." But 2014 is "warmer" than the "next warmest year" by a difference of 0.02°, while the error in temperature measurements is 0.5°. That means, in fact, that 2014 isn't warmer at all. To the significance known, every year since 1997 is exactly the same temperature. Their differences are purely nominal. In fact, within the range of significance, 2014 could actually be one of COLDEST years since 2000.
One of my profs did this: He gave some silly math problem and wrote to answers on the board. One was 3.6 and one was 3.6454265 (or something like that). Neither answer was correct, but the entire class believed the second was correct. He was teaching us how to BS.
However, using a 2-sig-dig constraint to restate 12,450 to 12,000 makes quite a bit of real world difference if the units are "ounces of gold."
Throw away the homework. Go out and play!