-- Sixteen days ago, Katie Heenan's father countered her frustration with simple mathematics. As she pondered taking a hiatus from gymnastics after failing to advance to this weekend's Olympic team trials because of a devastating fall at the U.S. championships in early June, John Heenan pulled out a calculator.

Train for two more weeks, he told her after a strategy session with Heenan's mother in a fast-food restaurant in Burke. You've already spent 28,000 hours and 700 weeks training since you were 4 years old. What's another 80 hours and two more weeks? An opening could come along, he insisted. You have to be ready.

"I was trying to help her put the whole thing in context," John Heenan said. "It had been her lifelong dream. . . . I asked her: Why not go one-tenth of a percent more?"

Katie Heenan, who trains at the Capital Gymnastics Training Center in Burke, said the discussion did two things: It made her laugh, and it changed her mind.

"I decided I should keep training on the off-chance I would get in," she said. "If not, I might regret it the rest of my life."

Last Friday, while driving her '98 red Beetle to a physical therapy appointment in Washington, she got a call from her coach, Tatiana Periskaia, who told her, "You're in!" Another competitor, Nicole Harris, had withdrawn from the trials because of an ankle injury.

Ashley Postell of Burke, who finished a spot ahead of Heenan, had not been training, so the opening went to Heenan, 18. On Friday, she and 15 other women, including U.S. co-champion Courtney Kupets of Gaithersburg, will compete in the preliminary round of the trials. Though the event will not determine the U.S. Olympic team, it is a significant part of the competition for six Olympic team positions that will be in large part distributed by women's national team director Martha Karolyi.

The men's preliminaries took place late Thursday night at Arrowhead Pond.

Because of her performance at nationals, Heenan could fairly be described as a long shot. She is, however, elated to have any shot at all.

"I'm trying this competition to do it more for myself," Heenan said. "I'm not going to try so hard to prove myself to Martha, the people in charge of picking [the Olympic team]. . . . I can't lose anything. I can just gain everything."

At the U.S. championships, Heenan seemed certain to make the top 12, which would have guaranteed her an invitation to the trials. But on her last -- and best -- event, the uneven bars, Heenan fell while attempting to dismount. She finished 14th.

"Everything came to an end so abruptly," said Heenan, who plans to compete for the University of Georgia this fall. "I wasn't prepared for that. Also, to think bars are my best event. It was more of a shock than disappointment."

Heenan's finish surprised many. Having overcome a broken heel in 1999 that required two surgeries and took a full year to heal, Heenan won national titles on the uneven bars last year and in 2001. She also won a bronze medal in the event at the 2001 world championships, shortly before succumbing to a sore back that put her in a body brace for six months.

Heenan's parents were so certain she would advance to the trials, they booked plane tickets for themselves, her two younger brothers and maternal grandmother for Anaheim well before the U.S. championships. After nationals, they were stuck with $900 in plane tickets they thought they couldn't use, so they canceled them.

Last Friday, John and Lisa Heenan sat side-by-side with laptops, searching for relatively inexpensive fares to Anaheim as the midnight deadline for seven-day advance purchase sales approached. They found they couldn't reuse their old tickets, so they bought new ones on a different airline -- and at a higher cost. All told, they had spent well over $1,000 on their Anaheim adventure. But this was another case in which John Heenan got out his calculator and did not hesitate.

He recalled his daughter's words on her cell phone, when she passed on her good news earlier that day.

"She just screamed for joy," John Heenan said, adding that she told him: "You know what, Dad? It happened. Your math was right."