At the close of the NASDAQ and New York Stock Exchange trading days, Apple had a market capitalization of $344.21 $346.74 billion, narrowly edging behind Exxon at $344.09 $348.32 billion.

And with that, a company that was on the ropes in 1998 became the biggest publicly-traded company in the world. [At least temporarily.]

Update:An early version of this post used incorrect preliminary numbers to calculate the company’s market cap figures. This includes updated numbers for both Apple and Exxon from the NYSE and Nasdaq. —TC

It was an odd trading day; after yesterday’s big dive, and falling for most of the morning, the Dow Jones Industrial Average actually closed up for the day up 430.30 points, or 3.98 percent, at 11,240.15. According to Reuters’ Anthony De Rosa, “the DJIA picked up 630 points in the final 90 minutes. The day’s gain was the 10th largest run in history of the Dow.” The Nasdaq closed up 124.83 points, roughly a 5.29 percent gain.

Apple closed the day up 5.89 percent at a final share price of $374.01; Exxon was also up, but only 2.07 percent, closing at $71.64. In short, Exxon’s sharp fall yesterday coupled with Apple’s big gain today made up the difference. Google, Amazon and Microsoft all had gains roughly equivalent to Apple’s.

A company’s market capitalization or “market cap” is the price of each share of its stock multiplied by the total number of outstanding shares: For publicly traded companies, it roughly prices what the market judges to be the company’s total value.

Last summer, Apple’s market cap passed Microsoft’s, making Apple the world’s largest tech company. When asked at D8, Apple’s Steve Jobs shared his feelings about that milestone with AllThingsD’s Walt Mossberg and Kara Swisher:

For those of us that have been in the industry a long time, it’s surreal. But it doesn’t matter very much. It’s not what’s important. It’s not what makes you come to work in the morning. It’s not why any of our customers buy our products. So I think it’s good for us to keep that in mind, and just remember what we’re doing and why we’re doing it. But it is a little surreal.

If anything, it’s more surreal now, as the market sheds value, favoring some companies at the expense of others. On NPR’s Marketplace this morning, even before Apple’s rally, Kai Ryssdal observed that “Apple could buy Bank of America for cash and have $6 billion left over.”

The numbers are mind-boggling. Apple’s P/E, or price to earnings ratio, is still quite high at 14.7 compared to Exxon, Microsoft or Intel (9.30, 9.32, 9.34), but is much less than Amazon’s gaudy 89.54. The suggestion is that investors expect Apple and Amazon will continue to grow, while the other companies’ growth rate is effectively already priced in.

Given how mercurial the market’s been this week, it would probably be foolish to attribute too much to these numbers, especially too much stability. They’re not why we’re here. But it is one more scorecard, for those of us who care about keeping score.

What’s next for the House That Jobs Built? Why not one more surreal milestone? How about becoming the first $1 trillion company?