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An apostrophe often indicates a place in a word where a letter has been dropped (also called a contraction or elision). If you just remember this, you will be well on the way to figuring out these tricky spelling problems.
IT’S is a contraction of the words IT and IS, or IT HAS. They get pushed together, and the I from IS falls off (or the HA from HAS fall off), with an apostrophe put in to show where it used to be. It is fun to visit the ducks can be written as It’s fun to visit the ducks. Another example: It has been entertaining learning to swim in shark-infested waters can be written as It's been entertaining learning to swim in shark-infested waters. [Aside: Contractions are generally used in more informal speech and writing. If you were writing a formal essay or scientific paper, for example, you may need to avoid contractions.]
ITS (with NO apostrophe) is another one of those possessive adjectives, just like YOUR. It indicates possession, or ownership by a thing, animal or someone of unspecified gender (if something belonged to a man or boy, it would be HIS, and if something belonged to a woman or girl, it would be HERS). For example, The dog didn’t like wearing its ruffled collar. The ruffled collar belongs to the dog (even though it would probably like to lose it!).
One of the reasons people get so confused with ITS is that it is an exception to the rule - many other possessives use an apostrophe S to indicate ownership (George's hat, Sally's flamethrower, New York's festival, the dog's pet frog). But for the neutrer case (ie it not having a gender associated with it), ITS is the possessive, with an S, but without an apostrophe! We freely admit it makes no sense. Although his, hers, and theirs are possessive pronouns that end with S too, and they don't have apostrophes either.
To decide which spelling to use, say the words “it is” in the sentence to see if it makes sense. If it does, then you use IT’S, if it doesn’t, use ITS.
For example, It’s good to see my pet duck eating it’s dinner. Now, say “it is” for each of the instances: It is good to see my pet duck eating it is dinner. It is good makes sense — so it is can be contracted to IT’S. However, my pet duck eating it is dinner doesn’t make sense — the dinner does belong to it (possessive), so the correct usage in this case is ITS.
If you still have trouble with the difference between ITS and IT'S, or even if you sometimes make careless mistakes, then you can use editing software to help you. For example, the popular software StyleWriter by Editor Software will check commonly confused words, including ITS and IT'S. For $150, the software is an excellent tool for double checking that you have made no careless mistakes. It is also an excellent plain language tool. Another excellent editing program is RightWriter. RightWriter is almost as good as StyleWriter and costs only $29.95.