How safe is opening any website on new browser tab?


When I do online shopping where I use my credit card information to purchase, I clear the browser cache, cookies and only open that single site. After I am done, I again clear the cache, cookies and start with my regular browsing. I do this to ensure any other websites that I open on a new tab do not sneak into my credit card information. Is this even possible or just a myth?

So if I wish to open "any" site on a new tab while doing my online shopping, is it safe or do I have to clear cookies every time and open only one site?