Targeting many keywords gives you the chances of gaining more visitors and popularity because people search in different terms with more keywords and phrases.
Then targeting long tail keywords can bring in more targeted visitors, genuine customers and insure conversion.

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^ Yep you're right! But we must avoid this what we call "keyword stufffing". It will not help us and in fact, it will only lessen the effect of our keywords and we're going to have poor rankings in SERPs while using our targeted keywords. We must consider the "singular" and "plural" forms of the word. As we all know, singular and plural form of a word can give us two diffrent results in SERPs. We can also consider targeting "long-tail" keywords. Usually, long-tail keywords doesn't have high competition and in that way, we can gain decent rankings in SERPs using those LT keywords. And by the way, keyword generating tool such as Google Adwords can help us to analyze and picked the most appropriate keywords that will suite in our site/webpages. :)

Long tail keyword phrase is really beneficial and i think it is genuine traffic to your site.

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Yep though usually, they are not that highly searched compare to one-word keywords yet very helpful especially to new sites wherein their website is on a very competitive niche/environment. :)