Whenever I really get to thinking about it, one person's life isn't really all that significant in the grand scheme of things. The city/town I live in has around 100,000 people altogether. That's 100,000 individuals, each with their own personalities, aspirations, and actions. 100,000 people each at the center of their own universe. And even the whole city is only a tiny speck on a map of the world. The world itself, even, revolves around the sun, which itself is a tiny speck of light in our galaxy, which itself borders on insignificance in the vastness of the space around it. All of the actions and interactions and personality traits and thoughts and emotions of any single person could be brought together and added up, and in the context of all that is, it would be so infintesimally small that it may as well not exist at all.
You could easily consider this in a very grim and opportunistic light. If my life doesn't matter in the grand scheme of things, then what's the use in living it well? Why shouldn't I just work to serve my own interests, my own desires, my own entertainment? After all, no matter how horrible a deed I commit, when weighed in the context of the universe, it basically didn't happen. Chaos theory would say that that action can have consequences that have their own consequences, et cetera, et cetera, et cetera, until the end product is something much more significant. But if every action starts a similar chain of events, then there are so many actions going on all the time and starting such chains that a single one of them is still insignificant. You could justify just about anything you do in this way.
The problem is that it's irrational in the first place to consider your life in the context of all that is. The human mind cannot truly imagine the vastness of even something so simple as the number of people on earth: 6.5 billion. That's 6,500, a thousand times over, a thousand times over, people. In the broader picture of the universe, scientists can only explain distances in light years, which are just under 6 trillion miles. The human brain is simply not capable of comprehending these numbers; that's why we have to break them down into units we can easily calculate and talk about: thousands, millions, billions, trillions. The simple fact that the units in all that is are so vastly different from the units involved in day-to-day life shows that you cannot consider the two together. You can either consider the whole universe, and not even think about each individual person (including yourself) at all because they're so insignificant; or you can consider each individual person, and not think about the universe as a whole because it so hugely dwarfs the individuals that you cannot clearly look at them. An individual cannot be thought of in the context of the universe any more than the universe can be thought of in context of individuals.
So we can only really think of ourselves in a context we can more clearly comprehend: Our immediate environment, and all the people we come into contact with. In such a context, I think it's worth it to try to live a good life. Who cares that all the good I could possibly do in my life isn't significant in the grand scheme of things? It's significant to my world, and it's significant to the world of each person who is affected by it.
If I impact a single person in a positive way, no matter how small it is, it's significant. The same holds true for negative impacts. And you really can't avoid having negative impacts on some people. I know I've hurt people in the past, and I know I'll hurt people in the future. That's just the way life is. But I'd really like, when I'm old and see death approaching, to be able to look back and see that I've left an overall positive impact on this world. I'd like to know I've helped people far more than I've hurt them.
My life will be significant, even if not in the context of the universe. I'd like it to be significant in a good way.