There's a lot of context that goes into deciding which digits are significant. I like to use the "anger management method" for deciding which digits are significant.
Suppose you are shopping for a fancy television. You see an advertisement that there's one you like on sale for \$1369.99. You know that your area has 10% sales tax, so you predict that when you buy the television your total will be about \$1500. You buy the television, and your actual total is \$1506.98. Are you mad about that extra seven dollars? Probably not — in which case the trailing zeros in your estimate were not significant.
The next week, the water main in your front yard fails and your yard fills with water. Your plumber digs a trench in your yard and replaces the pipe, and you write him a check for \$1500. When your bank statement arrives you notice that the bank actually debited \$1506.98 when it honored the check. Are you mad about that extra seven dollars? Goddamn right you're mad! You'll probably double-check the copy of the check to make sure you wrote it correctly and it wasn't modified on its way to the bank, and you probably won't use that plumber again. In that case the trailing zeros were significant.
When in doubt in the physical sciences, you write the uncertainty explicitly: $1500\pm100$ or $1500\pm10$ or $1500\pm1$ or $1500.0\pm0.1$.
Supposedly when the height of Mt. Everest was first measured the altitude came to $29\,000\pm1\rm\,ft$. The surveyors thought that if they reported the height as $29\,000\rm\,ft$ then people would assume their measurement was sloppy, so the last digit was fudged and the altitude was reported as $29\,002\rm\,ft$.