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Everyone seems to have an opinion on what search engines consider to be the most important information on a web page. Be careful - there's lots of information on the web which is quite simply incorrect or misleading. I recently spotted an article suggesting that search engines think words in larger fonts are more important. This is an SEO myth that has been hanging around for years and I'm not sure how it began.
Search engines do not care about the visual design of your website as long as you present the same visual information to humans as you do to their spiders. The search engines use HTML programming tags to understand the different parts of a web page the way people use visual clues such as looking for bullet points, or skim reading for section headings or site navigation.
The <h1> heading tag is one of these programming clues which tells a search engine that the text is the main heading on the page and that the search engine should pay extra attention to whatever text is between the <h1> and </h1> tags. Simply using an <h1> programming tag implies that the text is important because the <h1> should describe the subject of the page; any styling you give your <h1> is merely window-dressing to make the text look nice for your human visitors.
The article does make a good point; it just gives the wrong reasoning: you shouldn't use a very small font size for any text on your page, but not because it will make search engines ignore your keywords. You shouldn't use tiny fonts because they are very hard to read. Many people will find even 8 point fonts too small. You should always use text sizes that won't make your readers struggle because they probably won't stick around long enough or even know how to enlarge the text.
Why is this important for SEO then? Search engines do not like to find text that humans will not be able to see any more than your visitors do.