How to use 整 as in exactly I"m trying to figure out the grammar/syntax behind using "整". I know that it means "Exactly" when used at the end of numbers, but I'm wondering does it come before or after the noun described by the answer? Example
 1. 三百八整人 
 2. 三百八人整 

Thank for all of your help!
整 should be used after the measure word, so 三百八整人 is not correct.

However, 三百八人整 is weird too. 整 is usually used at the end of the phrase to prevent from adding new numbers to change the whole meaning, especially in financial affairs. Such as

三元 -> you can change it to 三元五角八分
三元整 -> you can't change it to 三元整五角八分, which is wrong expression.

Originally 三百八人 can't be changed to 三百八人零点五人 and so on, so need not to add 整 after that.

BTW1: It also can be written as 正 in financial affairs.
BTW2: As @user58955 said, 三百零八人 is more natural than 三百八人.